Scattering of protons by hydrogen atoms at low energies: Phase shifts and differential cross...

ATOMIC DATA AND NUCLEAR DATA TABLES 25,287-310 (1980)

SCATTERING OF PROTONS BY HYDROGEN ATOMS AT LOW ENERGIES

Phase Shifts and Differential Cross Sections

GEOFFREY HUNTER and MARY KURIYAN

Centre for Research in Experimental Space Science York University, Downsview, Ontario M3J lP3, Canada

Phase shifts and differential cross sections for spin exchange (charge transfer) and total elastic scattering of protons by hydrogen atoms are presented for 36 and 38 values, respectively, of the collisional kinetic energy in the range 0.0001 to 10 eV (center of mass). The phase shifts are tabulated with a precision of six decimal digits. Each cross section is presented as a graph covering the complete angular range from 0 to rr radians (in center-of-mass coordinates). The phase shifts were obtained via partial wave analysis within a modified Perturbed-Stationary-States theory by calculations based upon very accurate (nonrelativistic) internuclear potential energies for the lSuz and 2Pu, electronic states of HZ. The cross sections demonstrate a transition from purely quantum behavior at very low energies (~0.1 eV) to semiclassical behavior at higher energies (> 1 eV) in which protons scattered by spin exchange are angularly separated from those scattered without exchange. Thus the in-principle unobservable charge-transfer cross section becomes physi- cally measurable at energies greater than about 1 eV.

0092-640X/80/040287-24$02.00/0 Copyright 0 1980 by Academic Press, Inc. All rights of reproduction in any form reserved. 287 Atomic Data and Nuclear Data Tables. Vol. 25, NO. 4. July 1980

GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV

CONTENTS

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 Phase Shifts . . . . . . . ..I.................................. 288 Differential Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

EXPLANATION OF TABLE AND GRAPHS . . . . . . . . . . . . . . . . . 291

TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

Both the Table and Graphs give values for the following 36 collisional energies in the center-of-mass system (eV):

0.0001 0.0036 0.0070 0.013 0.05 0.0005 0.0038 0.0080 0.014 0.10 0.0010 0.0040 0.0090 0.015 1.0 0.0015 0.0042 0.00% 0.016 2.7 0.0020 0.0046 0.0105 0.018 0.0024 0.0050 0.0110 0.020 0.0028 0.0055 0.0120 0.025 0.0032 0.0060 0.0125 0.030

In addition the Table gives phase shifts for 5.0 and 10.0 eV.

INTRODUCTION

The scattering of protons by hydrogen atoms is one of the few elementary collision processes for which the accuracy of theoretical calculations can surpass that of current experimental techniques. The results reported here were obtained by a computational theory whose feasibility and accuracy increase as the collisional kinetic energy decreases, whereas the feasibility of cross-section measurements decreases as the energy becomes very small. The lowest energy considered (0.0001 eV) corresponds to a translational temperature of 1.2”K; cross-section measurements at these very low energies are experimentally inaccessible, yet may be relevant to astrophysical observations. The highest energy (10 eV) is the approximate upper limit of feasibility for the computational theory. It is also just below the threshold (10.2 eV) for excitation of then = 2 states of atomic hydrogen. Thus only elastic scattering events are possible within our energy range. The results ef- fectively cover the range from essentially zero energy up to the threshold for the onset of inelastic collisions. The accuracy of the calculations is about six decimal digits as the tabulated phase shifts imply. The theory and computational method were described previously.’

Phase Shifts

The method by which the phase shifts were calculated was described previously1 and a few of the low- energy phase shifts were published (Table 2 of Ref. 1) together with the integrated cross sections. Phase shifts covering the whole energy range are presented in the Table given here. These are the basic scattering data produced by our Perturbed-Stationary-States calculations. They may be used to verify our calculated integral cross sections (Table 3 of Ref. 1) and also the differential cross sections in the Graphs. They are also the data required for the calculation of other cross sections such as those for scattering of polarized protons by polarized hydrogen atoms.3

The tabulated phase shifts will be particularly useful when comparison with experiment is required, since experimental arrangements never achieve the ideal of measuring a totally integrated cross section at a precisely defined energy, nor a differential cross section resolved at a precisely defined angle. Experi- ments always correspond to a partially integrated cross section, the integration being over an angular range

288 Atomic Oata and Nuclear Oata Tables, Vol. 25. No. 4. July 1280

GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.ooOl- 10 eV

and an energy range related to the resolution limits of the experiment.

The phase shifts are presented in the Table for 38 values of the collisional kinetic energy E covering the range E = 0.0001 eV to E = 10.0 eV. For each value of the energy there are two phase shifts for each value of the angular-momentum quantum number L. In principle L takes all integer values from zero to infinity. However, the phase shifts tend to zero as L tends to infinity, and thus the calculated cross sections converge at a finite value of L . The maximum values of L in the Table were chosen to yield cross sections with errors no larger than 0.1%; in many cases the errors are much smaller (as small as 0.001%). A discussion of truncation error and the means of compensating for it was presented previously. l

Two electronic states of Hz+ are involved in proton-hydrogen scattering below 10.2 eV. The ISU, state has gerade symmetry and the 2Pu, state ungerade symmetry; the gerade and ungerade phase shifts correspond to scattering in each of these electronic states. The ISa, and 2Pa, potentials used in the calculation of the phase shifts were published previously as Coo and C,,, respectively, in Table 1 of Ref. 1.

For each of the 38 energies the number of tabulated ungerade phase shifts is less than the number of tabulated gerade phase-shifts. This simplification of the Table was possible because the corresponding gerade and ungerade phase shifts (i.e. at the same energy and L) tend to become equal as L increases. Thus only the ungerade phase shifts that differ from the corresponding gerade phase shifts are tabulated. The equality of gerade and ungerade phase shifts for large L is illus- trated in the Table by printing both of them where this does not increase the size of the Table; e.g. for E = 0.0028 eV the L = 25-29 g and u phase shifts are both shown even though they are identical. The phase shifts were calculated by a method that produced them modulo 2~.

Differential Cross Sections

The formulas by which the differential cross sections are calculated from the phase shifts are given in Ref. 2 (Eqs. (16), (17), (25), and (26)). They are reproduced here for the convenience of the reader.

Ten components us* of the differential cross section are defined by

(Ts9p = - j2 ,; [Z* (21 + W[’ + l)Pl(COS fwl~(COS 0)

x sin vf sin $, cos (71; - sf,) (1)

withp andq = even (e) or odd (0) , and s and t = gerade (g) or ungerade (u). P,(cos 6) is the Ith Legendre poly-

nomial.4 The collisional angular-momentum quantum number is 1 or 1’; in the Table it is denoted by L in order to avoid confusion with the numeral 1.

K is the momentum defined by

K = [W - Coo(w)]“2, (2)

where W is the total energy and C,,,,(w) is the asymp- totic limit of the lSu, and 2Po; potentials in atomic units. While K is, strictly speaking, momentum, for the atomic units implicit in Eqs. (1) and (2) its value is also, in effect, that of a reciprocal length. The phase shifts are denoted by 7B and rj’ in Eq. (1).

The ten components defined by Eq. (1) are com- bined to form three components (r++(6), a--(@, and o+-(0), the + denoting singlet and the - the triplet scattering amplitudes.2 These three components are defined in terms of the ten components of Eq. (1) by

a++(8) = 0% + a?” + tap”,

u--(e) = ug + CT?” + 2ugq;,

u’-(6) = ug + cr$ + (2;: + um SU’ (3)

Finally the total elastic cross section uel and the spin-exchange cross section a,, are obtained from the three singlet-triplet components by

u,,(e) = (1/4){u++(e) + 3u--(8)}, (4)

use(B) = (1/4)(u++(@ + u--(d) - 2u+-(e)). (5)

The total elastic cross section uel is the cross section for scattering of a beam of unpolarized protons by unpolarized hydrogen atoms with a nonpolarizing detector. The spin-exchange cross section a, is the cross section for a beam of spin-polarized protons scattered from unpolarized hydrogen atoms, with the detector registering only scattered protons having spin opposite from those in the incident beam.

The spin-exchange cross section uS, has often been referred to in the literature as the charge-transfer cross section. The reason is that a theoretical approach that assumes that the protons are distinguishable par- ticles (thus tacitly neglecting the Pauli principle) allows one to calculate separately the elastic cross sections for scattering with, and without, transfer of the electron from the target hydrogen atom to the incident proton. For these two types of scattering one assumes spinless protons. The expression for scattering with exchange (i.e. with electron (=charge) transfer) obtained from this semiclassical theory turns out to be identical with the spin-exchange cross section given by Eq. (S).5

Since the Pauli principle does apply to protons, the charge-transfer cross section is, strictly speaking, unobservable. However, the semiclassical theory

289 Atomic Data and Nuclear Data Tables. Vol. 25. No. 4. July 1980

GEOFFREY HUNTER and MARY KURIYAN

based upon distinguishable protons leads to the con- cept that protons scattered with electron transfer will appear roughly perpendicular to the incident proton beam (at approximately 8 = 7~ in center-of-mass coordinates), whereas protons scattered without electron transfer will appear close to the incident direction. The latter are virtually unobservable because it is difficult to resolve them from unscattered protons. Hence most experimental and theoretical work has been concerned with the charge-transfer process.

The differential cross sections presented in the Graphs now reveal how an in-principle unobservable quantity becomes, nevertheless, observable even in an experiment that employs unpolarized protons. As the collisional energy increases a, tends to zero in the angular region 8 = 0-7r/2 (0-7r/4 in laboratory coordinates), being concentrated in the complementary region of space (7r/2-m, ?r/4-?r/2 in laboratory coordinates) with maximum value (per unit solid angle) close to 7~ (7r/2 in the laboratory). Furthermore the total elastic cross section uel (which includes scattering with and without spin exchange, i.e. with and without electron transfer) tends to zero near ?r/2 (7r/4 in the laboratory), being concentrated in two regions spatially centered about 8 = 0 and 0 = rr (7r/2 in the laboratory), and as the energy increases the latter part of a,] (i.e. in the region about 8 = ?r) tends to become identical with a,. Thus protons scattered with spin exchange become spatially separated from those scattered without exchange. At sufficiently high energies an experiment with polarized protons and a polarizing detector will yield the same result (in the 8 = 7r/2-7r region) as a simpler experiment with unpolarized protons.

While vindicating the semiclassical theory of the charge-transfer cross section for energies greater than about 1 eV, the differential cross sections of the Graphs reveal the need for careful control of the acceptance angle of the detector. Even at 2.7 eV the detector should collect throughout the cone 8 = 7r/4 (in the laboratory coordinates) in order to measure the integrated cross section &.; it is not sufficient to collect within a small solid angle centered on 8 = 7r/2 except at very high energies.

Proton Scattering by H Atoms, O.OOOl- 10 eV

A considerable amount of computation is involved in the calculation of the differential cross sections from the phase shifts of the Table. One reason is that each of the ten components defined by Eq. (1) involves a double summation over L; the integral cross sections involve only a single summati0n.l As the number of significant phase shifts increases (with increasing energy) the number of terms in the double summation becomes very large. Furthermore these ten double summations (for a single energy) must be re- peated for many values of the scattering angle in order to generate detailed plots of the cross sections. Since the number of maxima in the cross sections increases with increasing energy the number of plotted values of 8 increases correspondingly. The differential cross sections were not plotted at the two highest energies because of the anticipated high cost of the computations.

The computer time involved in the calculation of the differential cross sections of the Graphs was about five times larger than that needed to calculate the phase shifts of the Table. Thus quite apart from the convenience of having plotted cross sections to look at, the computing involved justifies the presenta- tion of the Graphs as well as of the Table, even though the former is derived from the latter by a straightfor- ward computational procedure.

References

1.

2.

3.

4.

5.

G. Hunter and Mary Kuriyan, Proc. Roy. Sot. London A 353, 575 (1977)

G. Hunter and Mary Kuriyan, Proc. Roy. Sot. London A 341, 491 (1975)

S. Geltmann, Topics in Atomic Collision Theory (Academic Press, New York, 1969)

H. Margenau and G. M. Murphy, The Mathematics ofPhysics and Chemistry (Van Nostrand, Prince- ton, N. J., 1956), 2nd ed., Chap. 3

F. Masnou-Seeuws and A. Salin, J. Phys. B Ser. 2 2, 1274 (1969)

290 Atomic Data and Nuclear Data Tables. Vol. 25. No. 4. July 1980


EXPLANATION OF TABLE AND GRAPHS

TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms Energy Collisional kinetic energy in electron volts in center-of-

mass system K Momentum number occurring in the expressions for the

cross sections in atomic units (&,v’/*)-~. See Eqs. (1) and (2)

wade (g) Phase shifts for scattering by the 1 ,!$a, state of Hz in radians ungerade (u) Phase shifts for scattering by the 2Pu, state of Hz in radians L Collisional angular-momentum quantum number

GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms E Collisional kinetic energy in electron volts (Je1 Total elastic differential cross section defined by Eq. (4).

This cross section has a very high maximum close to 8 = 0. This peak is shown as an inset with the remain- ing part of the cross section plotted on a larger scale.

@se Spin exchange (charge transfer) differential cross section defined by Eq. (5)

Note Each of the cross sections is multiplied by sin(e) to produce an ordinate proportional to the total intensity scattered around the circle 19 = constant (4 = 0-27r). Thus the area under the plotted curve is equal to the corresponding integrated cross section Q,,, or Qse, which are given by’**

Qd

Qse

= $fey (21 + l)[sin* qf + 3 sin* @] 1

odd

+ 2 (21 + l)[sin2 q,I” + 3 sin* qf]},

= $- t (21 + 1) sin* (@ - $). 1 Cl

291 Atomic Data and Nuclear Data Tables. Vol. 25, No. 4. Juty 1080

GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.OOOl- 10 eV

TABLE. Phase Shifts for Scattering of PrQtons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs

Energy = 0.0001 eV K L: 0.082146 Number: gerade

LEO-9 g 4.247439 5.056802 4.671842 3.499711 0.142018 0.070979 u 2.275753 3.140749 3.298945 0.596268 0.139854 0.070977

L=lO-19 g 0.009636 0.007318 3.147282 3.146104 0.003637 0.002975 L=20-24 g 3.142876 3.142705 0.000970 3.142444 3.142343

Energy = 0.0005 eV K = 0.183684 Number: gerade

L:O-9 g 2.287448 3.369113 3.925411 3.894835 3.308923 0.442889 u 0.395738 1.550599 2.259844 2.407556 1.278369 0.429888

L-10-19 g 0.048627 0.036825 3.170169 3.164223 0.018232 0.014906 u 0.048627 0.036825 0.028577 0.022631 0.018232 0.014906

L.20-29 g 3.148014 3.147157 0.004853 3.145852 3.145350 0.003332

Energy = 0.0010 eV K I 0.259768 Number: gerade

L.O-9 g 1.134537 2.304650 3.060045 3.369195 3.150411 1.416588 u 5.557853 0.515917 1.410479 1.911494 1.861639 1.066588

L--10-19 g 0.098404 0.074241 3.199069 3.187039 0.036575 0.029882 L=20-29 g 3.154445 3.152728 0.009712 3.150114 3.149111 0.006666 L.30-31 g 3.145485 0.003533

Energy = 0.0015 eV K = 0.318150 Number: gerade

Lzo-g g 0.341983 1.554635 2.400355 2.856658 2.854744 2.035587 u 4.793209 6.077645 0.781964 1.445360 1.717157 1.447984

L=lO-19 g 0.149444 0.112281 3.228305 3.210048 0.055033 0.044928 u 0.149429 0.112279 0.086713 0.068455 0.055033 0.044928

Ln20-29 g 3.160886 3.158307 0.014576 3.154381 3.152874 0.010002 L-30-33 g 3.147433 0.005301 3.146418 3.145998

Energy D 0.0020 eV K = 0.367368 Number: gerade

L-0-g g 6.000642 0.956446 1.857998 2.403845 2.542455 u 4.194616 5.506759

2.095146 0.269545 1.031474 1.470808 1.504169

L.lO-19 g 0.201991 0.151006 3.257893 3.233252 0.073607 0.060046 u 0.201846 0.150986 0.116297 0.091659 0.073607 0.060046

L:20-29 g 3.167337 3.163892 0.019445 3.158651 3.156640 0.013341 L=30-32 g 3.149380 0.007068 3.144285

Energy = 0.0024 eV K :: 0.402431 Number: gerade

L=O-9 g 5.575605 0.546718 1.479682 2.077538 2.298334 2.021708 u 3.788621 5.117137 6.197308 0.732154 1.260627 1.444149

L=lO-19 g 0.245431 0.182571 3.281840 3.251963 0.088552 0.182482

0.072193 u 0.244885 0.140234 0.110369 0.088551 0.072193

L-20-29 g 3.172504 3.168366 0.023344 3.162070 3.159655 0.016013 u 0.030912 0.026773 0.023344 0'.020477 0.018062 0.016013

L.30-31 g 3.150939 0.008483

Energy = 0.0028 eV

L-0-g g 5.197608 0.180845 1.138782 u 3.427494 4.769252 5.877053

LslO-19 g 0.290457 0.214782 3.306076 u 0.288882 0.214492 0.164431

L-20-29 g 3.177678 3.172843 0.027245 u 0.036085 0.031251 0.027245

L=30-39 g 3.152498 o.oOg8g8 3.150603 L:40-49 g 0.004653 0.004324 0.004026 L:50-59 g 0.002399 0.002262 0.002135 L.60-69 g 0.001395 0.001328 0.001265 L=70-79 g 0.000876 0.000853 0.000812

Energy = 0.0032 eV

= 25 ungerade I 10

0.041822 3.168451 3.159902 3.154645 0.041822 0.026858 0.018309 0.013052 3.144057 3.143658 0.001747 0.001491

= 30 ungerade = 14

0.225943 3.281224 3.235210 3.207770 0.225801 0.139612 0.093617 0.066178 3.153937 3.151931 0.008745 0.007464 3.153937 3.151931 0.008745 0.007464 3.144561 3.144248 0.002385 3.143743

= 32 ungerade = 10

0.513586 3.440895 3.334671 3.276385 0.508224 0.295324 0.192993 0.134787 3.166326 3.162299 0.017511 0.014942 3.147531 3.146905 0.004772 3.145895

= 34 ungerade = 14

0.857392 0.312702 3.442325 3.347889 0.832932 0.470574 0.299333 0.206165 3.178760 3.172697 0.026296 0.022433 3.178760 3.172697 0.026296 0.022433

3.150503 3.149564 0.007160 3.148048

: 33 ungerade = 14

1.139556 0.523675 3.563675 3.423241 1.099999 0.657969 0.412909 0.280687 3.191240 3.183125 0.035102 0.029939 3.191240 3.183125 0.035102 0.029939

3.153476 3.152223 O.Oog548 3.150201

= 32 ungerade = 25

1.263218 0.607517 3.678495 3.487188 1.223627 0.801915 0.507335 0.342532

3.201258 3.191489 0.042162 0.035954 0.059665 0.049897 0.042162 0.035954

3.155856 3.154352 0.01146'0 3.151924 3.155856 3.154352 0.011460 3.151924

K L 0.434675 Number: gerade = 80 ungerade = 25

1.776895 2.062911 1.907492 1.307957 0.660036 3.823933 3.555149 0.455979 1.051971 1.342589 1.273815 0.925523 0.602021 0.405859 3.270817 0.103575 0.084387 3.211305 3.199873 0.049234 0.041977 0.129216 0.103573 0.084387 0.069712 0.058280 0.049234 0.041977 3.165491 3.162671 0.018687 3.158236 3.156481 0.013372 3.153648 0.023898 0.021078 0.018687 3.158236 3.156481 0.017372 3.151648 3.14<8;Y 0.007531 3.148504 ii.O063;8 6.005862 0.00;4;7 0.00;016 0.003754 0.003507 0.003281 0.003073 0.002883 0.002708 0.002547 0.002017 0.001908 0.001807 0.001717 0.001625 0.001547 0.001466 0.001206 0.OOli50 0.00108j 0.001649 O.OOlOOi O.OiOs68 o.oOOyii~ 0.000804 0.000801 0.000657 0.000803 0.000811 0.000824 0.000793

K = 0.464687 Number: gerade E 76 ungerade : 25

L:O-9 g 4.855447 6.132046 0.827404 1.498657 1.836756 1.774099 1.298595 0.684667 4.030130 3.627964 u 3.101131 4.453719 5.583783 0.198784 0.848808 1.220631 1.271059 1.018882 0.693409 0.469888

LnlO-19 g 0.337458 0.247772 3.330667 3.289837 0.118684 0.096631 3.221383 3.208276 0.056319 0.04800y u 0.333660 0.247020 0.188915 0.148214 0.118679 0.096630 0.079790 0.066684 0.056319 0.048010

L.20-29 g 3.182859 3.177326 0.031151 3.168914 3.165689 0.021362 3.160618 3.158612 0.015285 3.155372 u 0.041266 0.035733 0.031151 0.027322 0.024097 0.021362 3.160618 3.158612 0.015285 3.155372

L=30-39 g 3.154058 0.011313 3.151892 3.150995 0.008607 3.149492 0.007267 0.006701 0.006191 0.005732 L.40-49 g 0.005318 0.004942 0.004601 0.004291 0.004008 0.003749 0.003512 0.003295 0.003095 0.002Yll L+50-59 g 0.002742 0.002585 0.002440 0.002306 0.002181 0.002065 0.001957 0.001857 0.001764 0.001676 L=60-69 g 0.001594 0.001517 0.001446 0.001378 0.001314 0.001257 0.001201 0.001145 0.001094 0.001056 L=70-75 g 0.001006 0.000982 0.000956 0.000886 0.000885 0.000828

292 Atomic Data and Nuclear Data Table& Vol. 25. No. 4, July 1990


TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs

Energy = 0.0036 eV

4.541674 5.827077 0.540065 2.801150 4.163027 5.312283

0.387142 0.281634 3.355678 0.378905 0.279990 0.213694 3.188045 3.181813 0.035059 0.046452 0.040220 0.035059 3.155618 0.012729 3.153180 0.005983 0.005560 0.005177 0.003085 0.002908 0.002745 0.001793 0.001707 0.001627 0.001137 0.001085 0.001044

K = 0.492875 Number: gerade = 76 ungerade = 25

L=O-g

LzlO-19

L.30-39 Lr40-49 L.50-59 L=60-69 L-70-75

1.238738 1.619815 1.631279 1.254604 0.685341 6.240947 0.652372 1.088852 1.233207 1.078747

3.309056 0.133889 0.108926 3.231491 3.216699 0.167377 0.133873 0.108923 0.089898 0.075107 3.172340 3.168710 0.024038 3.163001 3.160742 0.030748 0.027117 0.024038 3.163001 3.160742

4.350405 0.777374 0.063418 0.063418

E;“3% . 0.054051 0.054051

0.017199 0.017199 0.006966 0.003482 0.001984 0.001235

3.152172 0.009684 3.150480 0.008176 0.007538 0.004828 0.004509 0.004218 0.003952 0.003707 0.002594 0.002454 0.002323 0.002202 0.002089 0.001551 0.001479 ;.;;;;;; 0.001349 0.001293 o.ooog95 0.000921 .


1.114850 1.514705 1.557945 1.223798 0.678046 4.568133 6.125627 0.556702 1.021087 1.205214 1.096753 0.815263 3.318755 0.141536 0.115096 3.236558 3.220919 0.177027 0.141508 0.115091 0.094965 0.079326

3.157097 3.157097 0.006449 0.003276 0.001884 0.001187

Energy = 0.0038 eV

L=O-g

L=lO-19

L=20-29

k::;-;;

+;

LZ7OI73

4.393988 5.683308 0.404132 2.658906 4.025653 5.183440

0.413489 0.298915 3.368362 0.401602 0.296601 0.226192

3.748961 0.565193 0.057076 0.057076

0.066973 0.066973 0.018155 0.018155

0.007353 0.003676 0.002og4 0.001303

3.190641 3.184058 0.037015 0.049048 3.184058 0.037015

3.156398 0.013437 3.153825 0.006315 0.005869 0.005464 0.003256 0.003070 0.002898 o.oo189j 0.001802 0.001717 0.001186 0.001155 0.001106

3.174054 3.170221 0.025376 3.164193 3.161808 3.174054 3.170221 0.025376 3.164193 3.161808

3.152759 0.010223 3.150974 0.008630 0.007957 0.005096 0.004759 0.004453 0.004171 0.003q13

3.157959 3.157959 0.006808 0.003457 0.001990 0.001245

0.002738 0.002596 0.00245j 0.002325 O.OO;riOg ;.W;; 0.001562 0.001491 0.001424 0.001364

Energy r 0.0040 eV

L-O-9 g 4.250792 5.544001 0.272553 " 2.522247 3.892318 5.058497

L=lO-19 g 0.441398 0.316438 3.381169 u 0.424294 0.313264 0.238749

L-20-29 g 3.193238 3.186304 0.038971 u 0.051645 0.044712 0.038971

Ls30-39 g 3.157178 0.014145 3.154469 L=40-49 g 0.006648 0.006178 0.005752 L=50-59 g 0.003427 0.003232 0.003050 L-60-69 g 0.001993 0.001897 0.001807 L=70-74 g 0.001274 0.001216 0.001152

K 5 0.519536 Number: gerade = 75 ungerade = 25

0.994898 1.411811 1.483890 1.188664 0.666390 6.013454 0.462711 0.952672 1.172763 1.107607

3.328518 0.149213 0.121280 3.241633 3.225143 0.186720 0.149167 0.121271 0.100039 0.083551

4.814909 0.849789 0.070531 0.070531

3.793167 0.596222 0.060102 0.060102

3.175769 3.171732 0.026715 3.165385 3.162874 0.034176 0.030139 0.026715 3.165385 3.162874

0.019113 0.019113 0.007740 0.003869 0.002204 0.001373

3.153348 0.010761 3.151468 0.009085 0.008377 0.005364 0.005010 0.004687 0.004391 0.004119 0.002882 0.002727 0.002582 0.002447 0.002321 0.001728 0.001648 0.001570 0.001501 0.001435 0.001112 0.00110g

Energy = 0.0042 eV K = 0.532366 Number: gerade I 78 ungerade = 21

Lzo-g g 4.112654 5.409458 0.145193 0.878340 1.311079 1.409401 1.150034 0.650895 u 2.390507 3.764119 4.937561 5.904199 0.370339 0.883887 1.136738 1.112039

Lzlo-19 g 0.471720 0.334216 3.394102 3.338350 0.156926 0.127482 3.246717 3.229373 u 0.446949 0.329960 0.251359 0.196457 0.156854 0.127467 0.105122 0.087780

~~20-29 g 3.195837 3.188552 0.040928 3.177484 3.173243 0.028055 3.166577 3.163940 u 0.054244 3.188552 0.040928 3.177484 3.173243 0.028055 3.166577 3.163940

L=30-39 g 3.157958 0.014853 3.155114 ~~40-49 g 0.006980 0.006487

3.153936 0.011299 3.151962 0.009539 0.008795 0.006039 0.005632 0.005261 0.004921 0.004611 0.004325

L=50-59 g 0.003599 0.003393 0.003203 L-60-69

0.003027 0.002863 0.002711 0.002569 0.002437 g 0.002092 0.001992 0.001898 0.001810 0.001727 0.001649 0.001576 0.001507

L:70-77 g 0.001325 0.001265 0.001217 0.001162 0.001179 0.001015 0.000974 0.000698

0.007166 0.003639 0.002095 0.001309

5.064040 o .8805g4 0.074092 0.074092

0.063131 0.063131

0.0200k9 0.020069

0.008127 0.007525 0.004063 0.003821 0.002315 0.001443

Energy = 0.0046 eV K = 0.557141 Number: gerade = 72 ungerade = 25

0.654665 1.115897 1.260034 1.064718 0.610318 5.693888 0.190254 0.745995 1.056605 1.104583 3.358234 0.172471 0.139946 3.256915 3.237849 0.216055 0.172315 0.139909 0.115315 0.096255 3.180916 3.176268 0.030734 3.168963 3.166073 0.039323 0.034675 0.030734 3.168963 3.166073 3.155113 0.012376 3.152951 0.010449 0.009634 0.006169 0.005762 0.005390 0.005049 0.004737 0.003315 0.003136 0.002969 0.002814 0.002669 0.001982 0.001891 0.001808 0.001726 0.001648

Leo-9 g 3.848958 5.152403 6.184687 u 2.139124 3.519217 4.706004

L-10-19 g 0.548218 0.370638 3.420377 u 0.492015 0.363379 0.276690

L=20-29 g 3.201039 3.193050 0.044845 u 0.059447 0.051457 0.044845

L=30-39 g 3.159519 0.016269 L=40-49

3.156403 u. 0.007646 0.007106 0.006615

?%782 . 33849;;; 0.081225 0.069196 0.081225 0.069196 0.021985 3.161410 0.021985 3.161410 0.008902 0.008242 0.004450 0.004186 L=50-59 i 0.003942 0.003716 0.003508 .._.__ __

L=60-69 g 0.002292 0.002182 0.002078 L=70-71 g 0.001461 0.0013g4

Energy = 0.0050 eV

0.002535 0 ;002409 0.001577 0.001512

K I 0.580859 Number: gerade : 69 ungerade = 20

L.O-9 g 3.599956 4.909386 5.954011 u 1.902173 3.288052 4.486713

0.442287 0.928736 1.111390 0.971516 0.559799 5.493243 0.016113 0.608560 0.968815 1.079809 3.378409 0.188195 0.152504 3.267159 3.246349 0.235777 0.187887 0.152422 0.125548 0.104753 3.184350 3.179295 0.033415 3.171349 3.168207 3.156290 0.013454 3.153939 0.011358 0.010472

5.702716 0.963449 0.088372 0.088371

4.047751 0.737331

L.lO-19 g 0.723241 0.408470 3.447688 " 0.536429 0.396734 0.302078

L.20-29 g 3.206248 3.197553 0.048765 L-30-39 g 3.161080 0.017686 3.157692 L-40-49 g 0.008311 0.007724 L=50-59

0.007191 g 0.004284

L:60-68 0.004039 0.003813

g 0.002491 0.002371 0.002259

0.075269 0.075297

0.001691

3.163136 0.008959 0.004549 0.002618

0.006706 0.006263 0.005859 0.005489 0.005149 0.003603 0.003408 0.003227 0.003058 0.002902 0.002155 0.002056 0.001951 0.001876 0.001794

Atomic Data and Nuclear Da ta Tables. Vol. 25, No.4.July 1980




LnO-9 g 3.306685 4.622654 5.680744 u 1.624042 3.016236 4.227814

LnlO-19 g 3.442685 0.458573 0.338930 u 0.590295 0.438299 0.3337gl

L=20-29 g .3.212769 3.203188 0.053669 u 0.071176 0.061595 0.053669

L=30-39 g 3.163033 0.019457 3.159304 k&o-$9 g o.oog142 0.008497 o.oO791o L=50-59 g 0.004713 0.004444 0.004194 L.60-69 0.002740 0.002609 0.002485 L.70-75

g g 0.001733 0.001655 0.001593

Energy = 0.0060 eV

L:O-9 g 3.030877 4.352461 5.422368 u 1.362792 2.760589 3.983580

LzlO-19 g 3.662576 0.513091 0.374093 u 0.640772 0.479519 0.365405

L=20-29 g 3.219299 3.208830 0.058579 u 0.077707 0.067237 0.058579

L=30-39 g 3.164985 0.021228 3.160916 t&l-4g g 0.009974 0.009269 0.008629 L.50-59 g 0.005142 0.004848 0.004576 L=60-69 g 0.002gEg 0.002846 0.002711 ~170-75 g o.oo18g5 0.001808 0.00171g

Energy = 0.0070 eV

Leo-9 f ;:5ggj gg;g ;:;#j

Islo-lg g 3.799449 0.643681 0.448496 u 0.724762 0.558994 0.'428380

Lr20-29 g 3.232397 3.220137 0.068415 u 0.090802 3.220137 0.068415

Lz30-3g g 3.168892 0.024773 3.164142 L-40-49 g 0.011637 0.010815 0.010069 IdO-59 g 0.005999 0.005656 0.005339 L.60-69 g 0.003488 0.003320 0.003163 L=70-70 g 0.002217

Energy D 0.0080 eV

L-O-9 g 2.065913 3.403637 4.507294 u 0.444753 1.860108 3.118737

t=lo-lg g 3.885379 0.830830 0.530550 u 0.779301 0.628795 0.490236

L-20-29 g 3.245556 3.231479 0.078273 u 0.103953 0.089885 0.078273

L:30-39 g 3.172802 0.028320 3.167370 L=40-49 g 0.013301 0.012361 0.011508 L=50-59 g 0.006856 0.006464 0.006102 L=60-69 g 0.003986 0.003795 0.003615 L170-75 g 0.002525 o.002398 0.002314

Energy = 0.0090 eV

L=O-g g 1.646883 2.990950 4.107084 u 0.042747 1.464699 2.736934

Lnlo-lg g 3.948082 1.158710 0.621479 u 0.803886 0.682772 0.547543

Ls?odg g 3.258817 3.242872 0.0881.58 u 0.117181 0.101268 0.088156

Lz30-39 g 3.176714 0.031869 3.170599 Lr4o-49 g 0.014965 0.013908 0.012948 Lsjo-59 g 0.007714 0.007273 0.006865 L-60-69 g 0.004484 0.004269 0.004067 ~~70-75 g 0.002839 0.002736 0.002588

0.190103 0.705059 0.928153 0.847314 0.486591 5.849825 4.192544 5.254551 6.089513 0.438482 0.852090 1.030929 0.983688 0.793359

3.404017 3.349703 0.168357 3.280046 3.257015 0.097328 0.082876 0.260526 0.207493 0.168172 0.138404 0.115412 0.097326 0.082876 3.188647 3.183080 0.036768 3.174334 3.170875 0.026296 3.165295 0.047054 0.041488 0.036769 3.174334 3.170875 0.026296 3.165295 3.157761 0.014801 3.155175 0.012495 0.011520 0.010644 ct.009855 0.007377 0.006890 0.006445 0.006038 0.005664 0.005321 0.005005 0.003963 0.003749 0.003550 0.003365 0.003192 0.003031 0.002881 0.002369 0.002261 0.002161 0.002063 0.001972 0.001882 0.001809 0.001525 0.001533 0.001439

K D 0.636299 Number: gerade

6.233857 0.491613 0.749144 5.028035 5.888026 0.271118

3.430032 3.369896 0.184405 0.285258 0.227191 0.184034 3.192947 3.186868 0.040124 0.051354 0.045276 0.040124 3.159233 0.016147 3.156411 0.008047 0.007517 0.007031 0.004324 0.004090 0.003873 0.002585 0.002467 0.002356 0.001636 0.001643 0.001425

K = 0.687282 Number: gerade

5.786412 0.089918 0.405951 4.606044 5.507791 6.229951 3.483606 3.410963 0.217051 0.334456 0.266548 0.215962 3.201559 3.194454 0.046841 3.201559 3.194454 0.046841 3.162178 0.018842 3.158884 0.009389 0.008770 0.008204 0.005045 0.004772 0.004518 0.003016 0.002878 0.002749

K = 0.734735 Number: gerade

5.374416 5.998183 0.081330 4.218002 5.153936 5.920829 3.540840 3.453117 0.250221 0.383566 0.305592 0.247799 3.210187 3.202051 0.053566 0.068594 0.060458 0.053566

3.165123 0.021538 3.161357 0.010732 0.010024 0.009376 0.005766 0.005454 0.005164 0.003447 0.003289 0.003142 0.002200 0.002175 0.001958

K e 0.779304 Number: gerade

4.993301 5.645953 6.054872 3.857150 4.821904 5.626281 3.603704 3.497411 0.283988 0.432439 0.344595 0.279324 3.218832 3.209659 0.060301 0.077239 0.068067 0.060301 3.168070 0.024235 3.163832 0.012074 0.011277 0.010549 0.006487 0.006136 0.005810 0.003878 0.003701 0.003534 0.002502 0.002496 0.002196

= 76 ungerade = 25

0.717522 0.405483 0.730425 0.967665

3.293043 3.267738 0.151340 0.126117 3.177320 3.173545 3.177320 3.173545 0.013632 0.012568 0.006587 0.006179 0.003671 0.003483 0.002251 0.002151

= 71 ungerade = 21

0.4 0381 0.4 0058 ii

0.2265 8 0.8126 5 8

3.319443 3.289418 0.177451 0.147694

3.183297 3.178888 3.183297 3.178888 6.015906 6.014665 0.007686 0.007209 0.004283 0.004063 0.002625 0.002510

= 76 ungerade = 25

0.184032 0.031746 0.228539 0.634988 0.204738 3.311486 0.203731 0.169496 3.189281 3.184235 3.189281 3.184235

3.159774 0.016762 0.008784 0.008240 0.004895 0.004644 0.003001 0.002872

= 76 ungerade = 25

6.208055 6.111528 6.264354 0.446484 0.231899 3.333881 o.229870 0.191389 3.1g5271 3.189588 3.195271 3.189588 3.162049 0.018860 0.009882 0.00927 1 0.005507 0.005224 0.003376 0.003230

5.908051 4.340849 0.983716 0.836282 0.106313 0.090498 0.106307 0.090497 0.028692 3.167454 0.028692 3.167454 0.011613 0.010752 0.005805 0.005459 0.003307 0.003143 0.002063 0.001965

5.902259 4.607 88 0.938010 0.881 05 8 0.124403 0.105805 0.124366 0.105796 0.033488 3.171776 0.033488 3.171776 0.013549 0.012545 0.006773 0.006370 0.003858 0.003667 0.002408 0.002297

5.824513 4.781800 0.849552 0.880645 0.142728 0.121234 0.142589 0.121193 0.038287 3.176099 0.038287 3.176099

0.015487 0.014339 0.007741 0.007281 0.004409 0.004191 0.002744 0.002626

5.713824 4.854741 0.733292 0.842963 0.161350 0.136854 0.160975 0.136717 0.043090 3.180426 0.043090 3.180426 0.017425 0.016133 0.008709 0.008191 0.004961 0.004715 0.003091 0.002953

294 Atomic Data and Nuclear Data Tables, Vol. 25, No. 4. July 1980



Energy : 0.0096 eV

L:o-g g 1.410451 2.758146 3.881352 u 6.098851 1.241204 2.520544

L:lo-lg g 3.974727 1.481019 0.681839 u 0.805397 0.706588 0.578073

L=20-29 g 3.266844 3.249745 0.094108 u 0.125165 0.108127 0.094101

L.30-39 g 3.179062 0.033999 3.172537 L.J+o-49 g 0.015964 0.014836 0.013812 L:50-59 g 0.008228 0.007758 0.007322 L.60-69 g 0.004783 0.004554 0.004339 ~~70-75 g 0.003032 0.002893 0.002779

Energy = 0.0105 eV

L=O-9 g 1.073461 2.426260 3.559515 u 5.775849 0.922838 2.211'jgg

L-lo-19 g 3.996710 2.080932 0.785019 u o.790781 0.730166 0.617125

Lr20-29 g 3.279009 3.260131 0.103072 u 0.137213 0.118467 0.103050

L=30-39 g 3.182587 0.037195 3.175446 L=40-49 g 0.017462 0.016228 0.015107 L=50-59 g L.60-69

0.008999 0.008485 0.008009 g 0.005232 0.004981 0.004746

L-70-79 g 0.003304 0.003172 0.003039

Energy = 0.0110 eV

L:o-9 g 0.894188 2.249642 3.388239 u 5.604366 0.753719 2.047275

L=lO-19 g 3.999417 2.358856 0.850598 u 0.774771 0.736984 0.635114

L-20-29 g 3.285828 3.265949 0.108079 u 0.143934 0.124240 0.108041

L.30-39 g 3.184545 0.038972 3.177062 L:40-49 g 0.018295 0.017001 0.015827 L.50-59 g L.60-69

0.009428 0.008889 0.008391 g 0.005481 0.005218

L.70-75 0.004971

g 0.003475 0.003329 0.003186

Energy I 0.0120 eV

L.O-9 g 0.551126 1.911306 3.059652 u 5.276949 0.430604 1.732770

L=lO-19 g 3.987177 2.702254 0.999369 u 0.728549 0.737345 0.662828

L-20-29 g 3.299556 3.277697 0.118175 u 0.157391 0.135844 0.118074


3.993263 4.708135 2

.201847 2.899001 3.927467

5.471878 5.505744 5.285577 .815123 5.558121 6.151659 0.308079

3.889301 3.648086 0.395343 0.317507 3.402244 3.359617 0.558454 0.458400 0.374223 0.307528 0.255999 0.215801

3.244953 3.232586 0.080564 0.071691 3.205677 0.057524 0.103327 0.090984 0.080562 0.071691 3.205677 0.057524

4.755800 0.592584 0.184757 0.183625

L=30-39 g 3.188465 0.042526 3.180296 3.176919 0.032332 3.171259 3.168880 0.025157 L--40-49 g 0.019959 0.018549

0.021518 0.017268

0.023245 0.016102 0.015039 0.014068 0.013179

Lr50-59 0.01028'6 0.009698 0.012363 0.011613 0.010923

g 0.009154 0.008649 0.008182 0.007747 0.007343 L260-69

0.006966 g 0.005979 0.005693

0.006149 0.006287 0.005423 0.005172 0.004936 0.004713 0.004502 0.004309

L-70-75 0.004119 0.003946

g 0.003782 0.003697 0.003481 0.003347 0.003154 0.002997

Energy = 0.0125 eV K = 0.918419 Number: gerade : 80 ungerade = 31

L:O-9 g 0.386819 1.749060 2.901737 3.842199 4.566234 5.070679 u 5.120292 0.275852 1.581953

5.354591 5.407337 5.208484 2.754217 3.790884 4.689246

4.715205 5.445782 6.056020 0.232314 0.539370

L.lO-19 g 3.973904 2.799606 1.080136 3.995228 3.676578 0.415303 0.332949 3.414211 u 0.699525 0.731166 0.672363

3.369155 0.192753 0.574385 0.475263 0.389720 0.320636 0.266741 0.224772 0.191339

Lz20-29 g 3.306430 3.283617 0.123269 3.249359 3.236434 0.083955 0.074700 3.208364 0.059933 0.054003 u 0.164096 0.141662 0.123115 0.107712 0.094825 0.083951 0.074699 0.066771 0.059933 0.054002

Le30-39 g 3.190425 0.044304 3.181913 0.048832 0.044304 3.181913

3.178394 0.033682 3.172498 3.170019 0.026207 0.024212 u 3.178394 0.033682 3.172498

0.022415 3.170019 0.026207 0.024212 0.022415

L-40-49 g 0.020792 0.019322 0.017988 0.016774 0.015667 0.014655 L.50-59 0.013728 0.012878 0.012097 0.011378 g L:60-69

0.010715 0.010102 0.009535 0.009010 0.008523 0.008070 0.007649 0.007256 0.006890 0.006549 g 0.006229 0.005930 0.005649 0.005386 0.005140

L.70-79 o.oo4go8 0.004692 0.004485

0.003949 0.003773 0.003618 0.004292 0.004105

g 0.003444 0.003067 0.003377 0.003227 0.003085 0.003115 0.002618

K I 0.804862 Number: gerade = 76 ungerade = 25

4.777785 5.444794 5.875239 6.056317 5.988469 5.637045 3.651724 4.631666 5.455847 6.118730 0.331218 0.654804 3.644862 3.525451 0.304845 0.248315 3.347391 0.172642 0.460980 0.368099 0.298191 0.245407 0.204469 0.172044 3.224028 3.214231 0.064345 3.198868 3.192802 0.045974 0.082434 0.072638 0.064345 3.198868 3.192802 0.045974 3.169839 0.025854 3.165317 3.163415 0.020119 0.018588 0.012879 0.012029 0.011253 0.010542 0.009889 0.009289 0.006g19 0.006545 0.006197 0.005874 0.005572 0.005292 0.004137 0.003947 0.003768 0.003602 0.003443 0.003297 0.002651 0.002569 0.002379

K = 0.841745 Number: gerade I 80 ungerade = 24

4.470446 5.156548 5.614146 5.833170 5.805219 5.511324 3.357314 4.357517 5.208192 5.904394 0.157425 0.529311

3.714377 3.569529 0.337467 0.273378 3.367704 0.189654 0.501263 0.403162 0.326657 0.268593 0.223910 0.188597 3.231843 3.221098 0.070419 0.062676 3.197627 0.050303 0.090245 3.221098 0.070419 0.062676 3.197627 0.050303 3.172493 0.028282 3.167545 3.165464 0.022008 0.020333 0.014088 0.013158 0.012308 0.011530 0.010817 0.010161 0.007568 0.007159 0.006778 0.006425 0.006095 0.005788 0.004525 0.004317 0.004123 0.003939 0.003768 0.003602 0.002903 0.002755 0.002758 0.002635 0.002349 0.002296


4.307033 5.002949 5.473527 5.711271 5.704585 5.437599 3.200320 4.210619 5.074526 5.787449 0.060881 0.456849

3.760335 3.594930 0.356338 0.287703 3.379062 0.199105 0.52.l835 0.422204 0.342563 0.281498 0.234622 0.197725 3.236198 3.224920 0.073797 0.065679 3.200309 0.052709 0.094595 0.083325 0.073797 0.065679 0.058716 0.052709 3.173968 0.029632 3.168783 3.166603 0.023057 0.021303 0.014759 0.013785 0.012895 0.012080 0.011332 0.010645 0.007928 0.007499 0.007101 0.006731 0.006385 0.006063 0.004740 0.004523 0.004318 0.004128 0.003947 0.003777 0.003046 0.002880 0.002825

4.863251 0.806438 0.146337 0.146093

0.017209 0.008737 0.005029 0.003151

4.84 875 a 0.73 616

0.160699 0.160209

xt;:; 0:018825 0.009557 0.005501 0.003445 0.002277

4.821001 0.691753 0.168719 0.168046

295 Atomic Data and Nuclear Data Tables. Vol. 25. No. 4, July 1980




L-O-9 g 0.226815 1.590976 4.967757

2.747703 3.694673 4.427556 0.125176

4.942433 5.239061 5.309486 5.131173 4.670281 u 1.435024 2.612990 3.657396 4.565803 5.335006 5.960882 0.155888 0.484256

L-10-19 g 3.956834 2.866569 1.162668 4.172784 3.707172 0.435587 0.348637 3.426484 3.378823 0.200745 u 0.667278 0.721079 0.678888 0.588661 0.491203 0.404821 0.333737 0.277557 0.233736 0.198999

L=20-29 g 3.313292 3.289553 0.128392 3.253789 3.240296 0.087353 0.077713 3.211052 0.062345 0.056173 u 0.170768 0.147479 0.128171 0.112111 0.098675 0.087345 0.077712 0.069459 0.062344 0.056173

L.30-39 g 3.192386 0.046083 3.183531 3.179870 0.035032 3.173737 3.171159 0.027257 0.025182 0.023313 u 0.050794 0.046083 3.183531 3.179870 0.035032 3.173737 3.171159 0.027257 0.025182 0.023313

Ln40-49 g 0.021625 0.02OOg6 0.018708 0.017445 0.016294 0.015241 0.014278 0.013394 0.012582 0.011833 L=50-59 g 0.011144 0.010506 0.009917 0.009371 0.008864 0.008393 0.007955 0.007547 0.007166 0.006811 L-60-69 g 0.006478 0.006167 0.005876 L.70-75

0.005603 0.005345 0.005106 0.004876 0.004662 0.004464 0.004278 g 0.004047 0.003924 0.003773 0.003597 0.003464 0.003267

Energy = 0.0140 eV K I 0.971963 Number: gerade = 80 ungerade = 29

L=O-9 g 6.202671 1.287041 2.450844 3.409394 4.158878 4.693969 5.013643 5.115491 4.976535 4.570381 u 4.674419 6.118400 1.151989 2.340432 3.399115 4.325920 5.118185 5.772482 0.001691 0.369409

LzlO-19 g 3.912995 2.941054 1.325451 5.329076 3.777717 0.478070 0.380331 3.451847 3.398765 0.216847 u 0.594838 0.690519 0.682761 0.611868 0.520217 0.433459 0.359539 0.299362 0.251756 0.214209

L;20-29 g 3.326949 3.301419 0.138703 0.121134 3.248073 0.094176 0.083753 3.216435 0.067168 0.060515 u 0.183973 0.159059 0.138301 0.120950 0.106409 0.094154 0.083747 0.074841 0.067167 0.060515

L=jo-39 g 3.196310 0.049641 3.186768 3.182824 0.037734 3.176216 3.173438 0.029357 0.027123 0.025110 ~~40-49 a 0.023291 0.021644 0.020149 0.018789 0.017548 0.016415 0.015377 0.014425 0.013550 ,0.012744 L.50-59 ;; 0.01~0~1 0.011315 0.01068t1 0.01009~ 0.009546 0.009039 0.008567 0.008127 0.007717 0.007334 L-60-69 g 0.006g77 0.006641 0.006327 0.006032 0.005755 0.005499 0.005254 0.005017 0.004811 0.004601 L=70-79 g 0.004415 0.004230 0.004069 0.003878 0.003740 0.003509 0.003509 0.003398 0.003309 0.002930

Energy = 0.0150 eV K = 1.006078 Number: gerade D 77 ungerade : 31

LsO-9 g 5.910722 0.998014 2.167910 3.136343 3.900556 4.454865 4.795852 4.924279 4.822006 4.461490 u 4.394858 5.842016 0.881872 2.079854 3.151440 4.094762 4.907574 5.587057 6.129840 0.249778

LnlO-19 g 3.857490 2.966535 1.475261 0.136603 3.865522 0.526396 0.412278 3.477756 3.419659 0.233423 u 0.513894 0.648371 0.674873 0.627180 0.545149 0.459772 0.384300 0.321844 0.270053 0.229447

Lt20-29 g "

L.30-39 g

L.40-49 : L-50-59 g L.60-69 g ~~70-76 g

3.340608 0.197018

3.313205 0.149032 0.130155 3.255931 0.170505 0.148398 0.129822 0.114189 0.053201 3.190006 3.185778 0.040437 0.053201 3.190006 3.185778 0.040437 0.023192 0.021590 0.020132 0.018803 0.012124 0.011443 0.010813 0.010228 0.007116 0.006780 0.006464 0.006168 0.004543 0.004543 0.004322 0.004163

3.178695 3.178695

3.221831 0.080234

0.017588 0.009685 0 .oo%892 0.004027

0.031459 0.029064 0.026906 0.031459 0.029064 0.026906

0.016476 0.009179 0.005628 0.003702

ergy = 0.0160 eV K : 1.039073 Numb er: gerade : 76 unge rade : 26

0.722443 1.897787 2.874765 3.651722 4.223766 4.585235 4.736718 5.577636 0.623259 1.829971 2.913347 3.871676 4.703005 5.404999 2.963632 1.602842 0.406176 3.975509 0.587308 0.445484 3.503566 '0.596915 0.656471 0.634014 0.565430 0.483658 0.407568 0.342470

0.064862 0.064862

3.200237 0.058644 0.024957 0.012859 0.007475 0.004736

0.014518 0.013655 0.008269 0.007859 0.005149 0.004940

En

5.632429 4.127610

L.O-9 g "

L-10-19 g U

4.347577 0.126681

0.250764 0.244872

3.441195 0.288498

Lr20-29 g 3.354530 3.324923 0.159291 0.139205 3.263866 0.107997 0.095931 3.227249 0.076840 0.069213 u 0.210014 0.181792 0.158393 0.138682 0.122003 0.107878 0.095931 3.227249 0.076840 0.069213

L=30-39 g 3.204167 0.056763 3.193246 3.188734 0.043141 3.181175 3.177998 0.033561 0.031005 0.028703 L=40-49 g 0.026623 0.024740 0.023031 0.021476 0.020058 0.018762 0.017576 0.016487 0.015487 0.014566 L=50-59 g 0.013717 0.012932 0.012207 0.011534 o.ologtl 0.010331 0.009791 0.009289 0.008820 0.008383 L.60-69 g 0.007973 0.007591 0.007232 0.006895 0.006581 0.006283 0.006001 0.005740 0.005492 0.005244 L.70-75 g 0.005047 o.004829 0.004628 0.004421 0.004287 0.004030

Energy = 0.0180 eV K= 1.102103 Number: gerade = 76 ungerade = 26

LnO-9 g 5.110412 0.205604 1.391052 2.382903 3.180670 3.782446 4.182179 4.374776 4.359083 4.112201 u 3.624753 5.079870 0.135742 1.357977 2.462276 3.447132 4.310870 5.051735 5.667922 6.157535

L-10-19

L:20-29

k=EB Go,-;;

- - L.70-75

.633526 .236106 .384156 .236437 0.204229

0.063896 0.027838

EX 0:005420

.770436

.594002 0.608419 0.623132 0.157107 0.156139

xi% 0:012977 0.007757 0.005115

4.288260 0.589220

0.523798 0.449448

3.556137 0.382169

m;i

0:037765 0.018550 0.010451 0.006458

3.483914 0.324553 0.086581 0.086581

EW 0:009924 0.006178

0.022568 0.012275 0.007402

0.122074 0.121720 3.186138 0.021110 0.011623 0.007069

0.108324 0.108324 3.182561 0.019775 0.011016 0.006754

-179613 .I77992 .I99731 .025914

:X33: .005332

.212040

.029957

:X: .005673

o.oogE31 0.005907

0.004820 o.oos6oi

296 Atomic Data and Nuclear Data Tablea. Vol. 25, No. 4, July 1950



Energy I 0.0200 eV

L-o-g g 4.671668 6.054479 0.965501 u 3.202051 4.661109 6.008116

L=lO-19 g 3.474168 2.827926 1.830315 u 0.053045 0.341161 0.514530

L.20-29 g 3.412282 3.372294 0.198572 u 0.260738 0.224916 0.195595

L.30-39 g 3.219176 0.070346 0.063998 u 0.077574 0.070344 0.063997

L--40-4g g 0.032966 0.030634 0.028517 u a.032960 0.030634 0.028517

L+jo-=jg g 0.016981 0.016010 0.015111 L.60-69 g 0.009871 0.009397 0.008952 k-/o-79 g 0.006237 0.005979 0.005735

Energy = 0.0250 eV

L.&g g 3.542976 4.935227 6.148880 u 2.115509 3.583361 4.948076

L-10-19 g 2.978538 2.485798 1.750401 u 5.786464 6.189276 0.202744

L=20-29 g 0.349287 3.439655 0.258048 u 0.325731 0.283781 0.247742

Lt30-39 g 3.240196 0.089224 0.081033 u 0.098372 0.089224 0.081033

L-40-49 g 0.041636 0.038688 0.036013 Ln50-59 g 0.021441 0.020214 0.019079 L.60-69 g 0.012461 0.011863 0.011302 L-70-79 g o-007879 0.007551 0.007242


Lzo-g g 2.603879 4.003037 5.230376 u 1.207713 2.681929 4.059420

L-10-19 g 2.480816 2.099731 1.505702 u 5.257762 5.741176 6.124283

L=20-29 g 0.448201 3.511683 0.313265 u 0.378296 0.333959 0.294118

L.30-39 g 3.260377 0.107781 0.097939 L.40-49 g 0.0499Bg 0.046447 0.043233 Ln50-59 g 0.025734 0.024261 0.022899 L=60-69 g 0.014955 0.014237 0.013564 Lrj'o-j'g g 0.009469 0.009042 0.008686


1.969978 2.783767 3.406529 3.835520 4.062967 4.085525 3.894067 0.959251 2.079905 3.085568 3.974660 4.745533 5.396770 5.927266 0.703295 4.714593 3.747986 0.616286 3.611705 3.522417 0.319255 0.589207 0.590324 0.545856 0.481102 0.414453 0.354806 0.303817 0.173082 3.293905 0.134755 0.119652 3.248243 0.095488 0.085888 0.171527 0.151364 0.134129 0.119267 0.106448 0.095399 0.085856 3.199991 0.053438 3.190618 3.186680 0.041562 0.038395 0.035542 0.058398 0.053438 0.049026 0.045088 0.041562 0.038395 0.035542

a.026590 0.024834 0.023229 0.021760 0.020412 0.019173 0.018033 0.026590 0.024834 0.023229 0.021760 0.020412 0.019173 0.018033 0.014279 0.013507 0.012789 0.012121 0.008536

0.011499 0.008145

O.Ologlg 0.010377 0.007778 0.007431 0.007110 0.006800 0.006510

0.005500 0.005285 0.005078 0.004880 0.004690 0.004510 0.004350

K r ?.298841 Number: gerade = 80 ungerade = 31

0.900515 1.755583 2.428649 2.917793 3.223281 3.340117 3.258483 6.209278 1.083264 2.135600 3.082158 3.921756 4.653032 5.274747 0.785794 5.715711 4.210994 1.146512 0.520385 3.670343 0.421633 0.398207 0.503063 0.536595 0.522346 0.480846 0.427816 0.374214

0.223969 3.336428 0.170878 0.151492 3.276995 0.121532 0.109333 0.216825 0.190625 0.168710 0.150333 0.134634 0.120959 0.108939

3.215454 0.067546 3.203541 3.198555 0.052503 0.048498 0.044892 3.215454 0.067546 3.203541 3.198555 0.052503 0.048498 0,044892 0.033579 0.031359 0.029333 0.027476 0.025774 0.024209 0.018028

0.022769 0.017052 0.016146 0.015303 0.014517 0.013785 0.013101

0.010778 0.010282 O.oog818 o.oog3Bl 0.008971 0.008589 0.008225 0.006927 0.006676 0.006334 0.006176 0.005931 0.005916 0.006659

L=O-9

LrlO-19

L:20-29

L:50-59 L.60-69

:=780"-78; L:90:99

L.lOO-100

B U

B U

Energy = 0.05 eV K=

5.960681 1.093869 2.355866 4.649888 6.139648 1.265153

0.621167 0.488596 0.193866 3.316535 3.989427 4.580326 2.812580 0.953958 3.869013 0.369854 0.388708 0.384907 3.344576 3.326014 0.168101 0.195836 0.178186 0.162287 0.084236 0.078272 0.072741 0.083865 0.077941 0.072496 0.042926 0.040466 0.038192 0.024935 0.023737 0.022614 0.015751 0.015101 0.014486 0.010591 0.010157 0.009837 ym; 0.007197 0.007030

.

0.002 71 5.339 il 97

0.885077 1.595062 2.131264 2.490633 2.671226 2.670864 0.239792 1.324922 2.311499 3.198842' 3.986187 4.672725

0.697267 5.921102 4.545988 2.685193 0.966428 3.900585 0.562822 0.127616 0.323954 0.439415 0.488258 0.490188 0.464280 0.423903

0.271498 3.380172 0.210187 0.185054 3.305151 0.145843 0.131240 0.259399 0.229176 0.203072 0.180386 0.160997 0.144548 0.130472 3.230753 0.081390 3.216125 3.210057 0.063068 0.058241 0.053903 0.040309 0.037645 0.035209 0.032981 0.030937 0.029058 0.027329 0.021637 0.020466 0.019378 0.018366 0.017423 0.016544 0.015723 0.012932 0.012339 0.011783 0.011259 0.010767 0.010301 0.009853 0.008311 0.008048 0.007622 0.007554 0.007234 0.007065 0.006456

1.836838 Number: gerade = 101 ungerade :: 50

3.463617 4.417448 5.217736 5.864%79 0.073734 2.592673 3.838902 5.003658 6.086766 0.804870

EZ69 . 0.564441 0.367836 3.294477 0.148041 0.067666 0.067514 0.036085 0.021561 0.013908 0.009651 0.007145

5.379764 4.559241 3.545860 2.297974 5.519878 5.872573 6.151306 0.077351 0.459071 3.526905 0.331859 3.431693 0.344010 0.317252 0.289691 0.262750 0.138739 0.126040 3.256637 0.105706 0.135327 0.124013 0.114006 0.105181 0.063051 0.058873 0.055086 0.051638 0.062973 0.058840 0.055075 0.051636 0.034136 0.032315 o.O;i626 O.Oi90;3 0.020572 0.019644 0.018770 0.017947 0.013348 0.012831 0.012322 0.011857 O.Oogl61 0.008802 0.008393 0.008182 0.006515 0.006281 0.006041 0.005801

0.411624 1.724198

0.847720 0.224111

E%go: . 0.097716 0.097354 0.048485 0.048486 0.027585 0.017173 0.011410 0.008004 0.005560

0.090668 0.090305 0.045591 0.045592 0.026215 0.016441 0.010997 0.007693 0.005320

297 Atomic Data and Nuclear Data Tables, Vol. 25. No. 4. July 1980



Energy = 0.1 eV K = 2.597682 Number: gerade I 147 ungerade = 73

6.169716 0.786002 1.553078 2.188734 5.656238 0.620891 1.804240 2.923188 3.019440 2.619948 2.087763 1.418635 2.684989 3.297152 3.848563 4.340205 4.776063 2.388038 5.356899 1.326143 6.282011 0.102835 0.177276 0.227357 3.457449 0.280776 3.393650 3.369691 0.244047 0.230459 0.216744 0.203043 0.128775 0.120975 0.113892 0.106925 0.125450 0.117585 0.110269 0.103389 0.068518 0.064999 0.061753 0.058704 0.068353 0.064825 0.061547 0.058464 0.041237 0.039344 0.037578 0.035921 0.041227 0.039344 0.037582 0.035924 0.026702 0.025654 0.024659 0.023716 0.026702 0.025654 0.024659 0.023716 0.018292 0.017659 0.017054 0.016482 0.013076 0.012679 0.012276 0.011924 0.009667 0.009419 0.009156 0.008903 0.007375 0.007185 0.007004 0.006825 0.005747 0.005614 0.005476 0.005353 0.004575 0.004476 0.004380 0.004279 0.003703 0.003592 0.003561

L=O-9

LzlO-19

L=20-29

L=30-39

L.40-49

L=50-59

L.60-69

L=70-79

L=80-89 L=90-99

yw;-;m;

LZl20-129 L.130-139 Ls140-146

1.234585 2.670207 3.970912 5.137192 0.019202 1.525372 2.966922 4.343868 3.317307 3.435921 3.426174 3.287318 5.895139 0.474987 1.274594 2.011081

2.694328 3.070521 3.977865 4.968444 0.608613 5.934937 4.773276 5.149637 0.890122 3.844310 0.258121 0.274018 0.207705 0.190315 0.189641 0.176740

0.099956 0.093232 0.096968 0.091090 0.055795 0.053003 0.055542 0.052772 0.034370 0.032906 0.034370 0.032906 0.022821 0.021969 0.022821 0.021969 0.015930 0.015393 0.011499 0.011199 0.008659 0.008424 0.006653 0.006485 0.005234 0.005114 0.004183 0.004103

B U

g U

4.821474 3.541610 2.074376 0.400325 5.471833 5.742663 5.965216 6.143411

g U

0.574716 3.623524 0.412469 0.358855 0.279115 0.276714 0.268846 0.257268 0.175269 0.161667 0.149138 0.138057 0.164588 0.153441 0.143302 0.134002

g U

g U

0.087050 0.081551 0.076701 0.072392 0.085754 0.080870 0.076357 0.072187

Number: gerade = 190 ungerade = 168

3.114529 4.226773 5.251148 6.189559 2.268483 3.662588 5.021640 0.062611

g U

0.050337 0.047818 0.045462 0.043271 0.050155 0.047695 0.045392 0.043239 0.031531 0.030231 0.028976 0.027808 0.031531 0.030231 0.028998 0.027808 0.021159 0.020389 0.019657 0.018958 0.014832 0.014406 O.Olj941 0.013480 0.010871 0.010550 0.010246 0.009951 o.oo8197 0.007980 0.007767 0.007557 0.0063% 0.006i82 O.OOab3i 0.005887 0.005001 0.004885 0.004778 0.004663 0.004028 0.003946 0.003862 0.003790

Energy = 1.0 eV K = 8.214591

0.760878 1.533639 1.352049 2.606973

5.186189 5.26449; 6.109538 0.752055 3.506928 3.060111 1.462491 2.099630 3.281089 2.38932; 0.440377 0.841076 5.207128 4.011134 3.599232 3.822654 3.227090 2.876071 5.261071 5.368054 1.154780 1.054416 6.005799 6.048698

L=O-9

L=lO-19

L.20-29

L=30-39

L.40-49

L=50-59

L-60-69

L-70-79

L=80-89

L=90-99

L=lOO-109

L.llO-119

L=120-129

4.040739 5.518352 0.619976 1.912733 2.622525 4.157877 5.657813 0.839198 2.226930 2.843118 3.384515 3.853352 3.827612 5.014216 6.167059 1.003247

5.284333 5.247184 5.154693 5.oo8095 1.646845 2.511138 3.345365 4.149975 2.566386 2.026513 1.440981 0.810470 2.710650 3.296067 3.856394 4.392235 1.455422 0.479894 5.746759 4.690788 1.221312 1.581721 1.922830 2.245256 2.842361 1.733344 0.718174 6.103807 4.031757 4.227172 4.409427 4.579184 2.572085 2.307428 2.075841 1.872336 5.466507 5.556952 5.639912 5.715821

B U

B U

g U

g U

g U

B U

B

U

8 U

8 U

g

U

B U

g U

g U

B U

g U

g U

g

U

0.964391 0.883560 0.810853 0.745268 6.087437 6.122389 6.153779 6.181924

0.431667 0.401784 0.374474 0.349592 0.026046 0.036681 0.045972 0.054054

L=130-139

L-140-149

0.225409 0.212991 0.201557 0.190941 0.084745 0.086495 0.087800 0.088734 0.135830 0.129969 0.124481 0.119419 0.087448 0.086549 0.085497 0.084370 0.091684 0.088564 0.085583 0.082816 0.075058 0.073625 0.072158 0.070681 0.066864 0.064966 0.063243 0.061599 0.061202 0.059900 0.058589 0;057321 0.051481 0.050391 0.049240 0.048007 0.049049 0.047944 0.046854 0.045818

L=150-159

L=l60-169

L=170-179 g 0.022235 0.021878 0.021528 0.021188 0.020851 0.020513 0.020179 0.019855 L=180-189 g 0.018927 0.018628 0.018327 0.018031 0.017743 0.017468 0.017201 0.016933

4.251944 2.089463 4.808849 4.925453

:-;::::tt . :‘::69% . 5.329861 4.737063 1.692-f91 5.785183 0.686136 6.207144

4.582497 3.142846

4.847017 4.163738 4.256774 0.107756 4.936521 5.858298 1.307312 3.106821 4.112590 5.019390 1.392693 5.906034

5.047630 5.152506

4.557988 5.672284

:*",;a;; . 2.467637 2.836684

:%::59: . 1.533830 5.848472

0.632692 6.229643

0.500688 0.46450; 6.283161 0.013854

0.253665 o.238950 0.079572 0.082428 0.148694 0.142029 0.088819 0.088184 0.098399 0.094936 0.077911 0.076489

4.130309 0.018569 0.122563 3.360802

;%:% . 1.266992 5.958335 0.540444 6.267436

0.326906 0.306109 0.287056 0.269640 0.060949 0.066837 o.071908 0.076135 0.181122 0.172116 0.163779 0.155958 0.089286 0.089540 0.089567 0.089321 0.114707 0.110248 0.106044 0.102097 0.083177 0.081903 0.080593 0.079271

0.080213 0.077664 0.075224 0.073010 0.069248 0.067862 0.066482 0.065100 0.059969 0.058376 0.056850 0.055374 0.056100 0.054881 0.053648 0.052433 0.046764 0.045591 0.044508 0.043492 0.044845 0.043913 0.042998 0.042097 0.037448 0.036651 0.035886 0.035186 0.036541 0.035771 0.035037 0.034339

0.040635 0.039791 0.039008 0.038239 0.039605 0.038842 0.038085 0.037311

0.070955 0.068904 0.063758 0.062473 0.053950 0.05264; 0.051269 0.050152 0.042510 0.041551 0.041226 0.040397 0.034540 0.03392; 0.033664 0.033015

0.028424 0.027782 0.027637 0.027127 0.022995 0.02260; 0.022995 0.022607 0.019540 0.019230 0.016674 0.01641~

0.033301 0.032668 0.030380 0.031429 0.032385 0.031758 0.031137 0.030520

0.030843 0.030271 0.029682 0.029067 o.o2gglO 0.029322 0.028748 0.028188 0.024818 0.024314 0.023843 0.023404 0.024722 0.024281 0.023842 0.023446

0.027147 0.026529 0.025931 0.025360 0.026635 0.026123 0.025645 0.025173

298 Atomic Data and Nuclear Data Tables. Vol. 25, No. 4,Juiy 1980

GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001- 10 eV

TABLE. Phase Shifls for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs


L-O-9 g 4.807064 0.012659 1.419841 2.746243 3.993058 5.161819 6.254343 0.989498 1.935887 2.812698 u 3.140238 4.680295 6.189641 1.385145 2.833262 4.250916 5.638243 0.712217 2.039397 3.336806

L.lO-19 g 3.622402 4.367518 5.050552 5.673986 6.240294 0.468690 0.927830 1.336777 1.697689 2.012574 u 4.604675 5.843257 0.769641 1.950488 3.102925 4.227280 5.323896 0.109942 1.152156 2.167725

L.20-29 g 2.283420 2.512083 2.700313 2.849839 2.962217 3.039016 3.081663 3.091556 3.070025 3.018321 u 3.157036 4.120487 5.058486 5.971448 0.576598 1.440718 2.281042 3.098004 3.892038 4.663565

L-30-39 g 2.937682 2.829248 2.694174 2.533514 2.348352 2.139682 1.908528 1.655847 7.382615 1.089770 u 5.413000 6.140770 0.564131 1.249880 1.915237 2.560615 3.186450 3.793163 4.381142 4.950788

L:40-49 g 0.778255 0.449014 0.102962 6.024251 5.647423 5.256656 4.852892 4.437148 4.010420 3.573757 u 5.502529 6.036765 0.270677 0.771035 1.255066 1.723131 2.175590 2.612846 3.035268 3.443187

L.50-59 g 3.128231 2.674935 2.215021 1.749632 1.280001 0.807344 0.332951 6.141294 5.667328 5.195575 u 3.836982 4.217024 4.583632 4.937156 5.277961 5.606357 5.922672 6.227259 0.237230 0.519271

L.60-69 g 4.727358 4.264025 3.806848 3.357128 2.916032 2.484720 2.064198 1.655417 1.259176 0.876157 u 0.790530 1.051293 1.301866 1.542562 1.773652 1.995437 2.208205 2.412215 2.607763 2.795110

L=70-79 g 0.506908 0.151818 6.094360 5.768276 5.456794 5.159789 4.877096 4.608414 4.353415 4.111683 u 2.974506 3.146239 3.310541 3.467656 3.617864 3.761363 3.898400 4.029240 4.154048 4.273079

L-80-89 g 3.882772 3.666212 3.461482 3.268095 3.085498 2.913206 2.750677 2.597428 2.452962 2.316804 u 4.386565 4.494656 4.597613 4.695627 4.788843 4.877519 4.961803 5.041850 5.117896 5.190058

Ls90-99 g 2.188504 2.067619 1.953732 1.846451 1.745383 1.650182 1.560503 1.476010 1.396428 1.321435 u 5.258503 5.323434 5.384949 5.443225 5.498419 5.550631 5.600033 5.646740 5.690865 5.732560

LzlOO-109 g 1.250782 1.184214 1.121464 1.062427 1.006694 0.954150 0.904629 0.857922 0.813882 0.772353 u 5.771907 5.809034 5.844065 5.877061 5.908161 5.937457 5.965001 5.990930 6.015315 6.038197

L-110-119 g 0.733169 0.696212 0.661339 0.628432 0.597375 0.568057 0.540384 0.514245 0.489565 0.466260 u 6.059711 6.079906 6.098825 6.116583 6.133220 6.148781 6.163358 6.176985 6.189713 6.201610

Lsl2O-129 g 0.444228 0.423420 0.403761 0.385164 0.367590 0.350978 0.335256 0.320386 0.306316 0.293007 u 6.212701 6.223047 6.232696 6.241659 6.250008 6.257777 6.264967 6.271646 6.277849 0.000382

Lz130-139 g 0.280399 0.268456 0.257168 0.246464 0.236296 0.226693 0.217599 0.208920 0.200725 0.192977 u d.005673 0.010573 0.015072 0.019219 0.023041 0.026529 0.029733 0.032675 0.035337 0.037755

Ls140-149 g 0.185572 0.178527 0.171917 0.165609 0.159614 0.153903 0.148495 0.143316 _. .__

0.042080 0.043859 0.045484 0.046930 0.048197 0.138383 0.133707

u 0.039973 0.049335 0.050337 0.051191 0.051938 Ls150-159 g 0.129262 0.125008 0.120946 0.117091 0.113420 0.109904 0.106576 0.103379 0.100328 0.097398

u 0.052588 0.053109 0.053535 0.053902 0.054169 0.054345 0.054468 0.054533 0.054527 0.054467 L1160-169 g 0.094597 0.091930 0.089366 0.086906 0.084574 0.082330 0.080148 0.078072 0.076117 0.074223

IJ 0.054402 0.054242 0.054036 0.053815 0.053558 0.053236 0.052892 0.052550 0.052176 0.051768 Lz170-179 g 0.072354 0.070583 0.068935 0.067311 0.065733 0.064222 0.062801 0.061404 0.060057 0.058756

u 0.051345 0.050908 0.050478 0.050002 0.049541 0.049069 0.048563 0.048034 0.047517 0.046910 L-180-189 g 0.057492 0.056268 0.055108 0.053989 0.052881 0.050839 0.049855 0.048861

u 0.046477 0.045961 0.0.51849 0.047914

0.045455 0.044971 0.044423 0.043912 0.043380 0.042843 0.042297 0.041765 L=190-199 g 0.047039 0.046197 0.045342 0.044476 0.043692 0.042911 0.042174 0.041471 0.040792 0.040107

u 0.041258 0.040836 0.040314 0.039797 0.039264 0.038794 0.038314 0.037816 0.037332 0.036871 L:200-209 g 0.039421 0.038770 0.038124 0.037574 0.036922 0.036335 0.035799 0.035239 0.034691 0.034154

u 0;036417 0.035941 0.035462 0.035038 0.034583 0.034126 0.033662 0.033208 0.032767 0.032336 L-210-219 g 0.033627 0.033122 0.032643 0.032169 0.031692 0.031216 0.030757 0.030321 0.029901 0.029505

u 0.031897 0.031450 0.031013 0.030601 0.030210 0.029815 0.029406 0.028993 0.028638 0.028266 L.220-229 g 0.029107 0.028722 0.028355 0.027927 0.027526 0.027091 0.026678 0.026275 0.025884 0.025518

u 0.027904 0.027542 0.027174 0.026853 0.026511 0.026192 0.025878 0.025556 0.025229 0.024911 L=230-239 g 0.025196 0.024924 0.024584 0.024350 0.024041 0.023752 0.023455 0.023177 0.022927 0.022569

u 0.024610 0.024324 0.024054 0.023777 0.023490 0.023202 0.022890 0.022601 0.022363 0.022127 L.240-240 g 0.022327

u 0.021874

299 Atomic Data and Nuclear Data Tables, Vol. 25. No. 4, July 1980



Energy = 5.0 eV K = la.368383 Number: gerade = 301 ungerade = 288

L=O-9 g 4.013988 5.507237 0.640203 1.980137 3.245137 U 2.630800 4.171661 5.682622 0.880562

4.436839 5.557183 0.325171 1.309544 2.229621 2.331951 3.753734 5.146073 0.225974 1.560027 2.465294

L-to-19 g 3.087979 3.887234 4.630000 5.318855 5.956315 0.261636 0.803547 i.301118 I.756499 2.171748 U 4.142046 5.390580 0.328026 1.521094 2.686951 3.825971 4.938541 6.025061 0.802756 1.838417

L=20-29 g 2.548812 2.889535 3.195674 3.468882 3.710727 3.922700 4.106198 4.262561 4.393046 4.498855 U 2.849281 3.835781 4.798345 5.737442 0.370305 1.263754 2.135044 2.984614 3.812907 4.620364

L=30-39 g. 4.581128 4.640944 4.679344 4.697302 4.695773 4.675643 4.637790 4.583030 4.512173 4.425975 U 5.407414 6.174480 0.638801 1.367175 2.076829 2.768161 3.441573 4.097468 4.736235 5.358246

L.40-49 g 4.325188 4.210518 4.082671 3.942305 3.790088 3.626641 3.452599 3.268548 3.075097 2.872804 U 5.963875 0.270316 0.844299 1.402982 I.946717 2.475858 2.990725 3.491640 3.978942 4.452939

L=50-59 g 2.662253 2.443979 2.218546 1.986467 1.748288 1.504506 1.255646 1.002192 0.744648 0.483490 U 4.913926 5.362218 5.798117 6.221894 0.350654 0.751060 1.140179 1.518279 1.885641 2.242502

L.60-69 g 0.219198 6.235424 5.966257 5.695339 5.423102 5.149991 4.876413 4.602802 4.329537 4.057035 U 2.589109 2.925730 3.252586 3.569911 3.877956 4.176928 4.467049 4.748554 5.021636 5.286508

L.70-79 g 3.785647 3.515765 3.247711 2.981853 2.718481 2.457930 2.200460 1.946370 1.695887 1.449274 U 5.543388 5.792457 6.033920 6.267977 0.211614 0.431399 0.644329 0.850566 1.050302 1.243697

LrBO-a9 g 1.206720 0.968450 0.734616 0.505403 0.280927 0.061333 6.129888 5.920329 5.715889 5.516637 U 1.430918 1.612136 1.787499 1.957174 2.121311 2.280056 2.433568 2.581977 2.725433 2.864077

L-90-99 g 5.322593 5.133786 4.950214 4.771867 4.598731 4.430757 4.267919 4.110138 3.957374 3.809530 U 2.998029 3.127442 3.252432 3.373124 3.489659 3.602135 3.710685 3.815430 3.916461 4.013914

L=lOO-109 g 3.666545 3.528321 3.394768 3.265797 3.141287 3.021163 2.905285 2.793573 2.685897 2.582151 U 4.107886 4.198472 4.285800 4.369948 4.451021 4.529128 4.604339 4.676764 4.746489 4.813588

LrllO-119 g 2.482233 2.386006 2.293392 2.204249 2.118486 2.035992 I.956644 1.880366 1.807022 1.736534 U 4.878167 4.940289 5.000042 5.057512 5.112757 5.165869 5.216911 5.265949 5.313068 5.358313

L=120-129 g 1.668796 1.603699 1.541173 1.481098 1.423403 1.367999 1.314785 1.263704 1.215096 1.168001 U 5.401762 5.443481 5.483510 5.521936 5.558799 5.594148 5.628064 5.660570 5.691729 5.721603

L=l30-139 g 1.122805 1.079409 1.037769 0.997798 0.959441 0.922630 0.887310 0.853417 0.820891 0.789688 U 5.750212 5.777626 5.803884 5.829014 5.853084 5.876116 5.898149 5.919238 5.939398 5.958677

Lrl40-149 g 0.759741 0.731016 0.703454 0.677002 0.651633 0.627284 0.603928 0.581528 0.560014 0.539388 u 5.977114 5.994723 6.011557 6.027638 6.042987 6.057655 6.071649 6.084998 6.097748 6.109898

L.l50-159 g 0.519589 0.500598 0.482374 0.464885 0.448110 0.432008 0.416550 0.401722 0.387497 0.373831 u 6.121481 6.132535 6.143058 6.153085 6.162644 6.171734 6.180392 6.188631 6.196463 6.203921

L.l60-169 g 0.360728 0.348144 0.336062 0.324490 0.313349 0.302647 0.292407 0.282538 0.273085 0.264101 u 6.211007 6.217730 6.224131 6.230200 6.235958 6.241444 6.246666 6.251509 6.256248 6.260625

L.170-179 g 0.255578 0.247184 0.239142 0.231409 0.223970 0.216826 0.209973 0.203379 0.197031 0.190943 u 6.264975 6.269315 6.273052 6.276572 6.279913 6.283055 0.002839 0.005639 0.008275 0.010758

L-180-la9 g 0.185087 0.179452 0.174031 0.169012 0.164003 0.159172 0.154545 0.150088 0.145783 0.141657 II 0.013098 0.015293 0.017343 0.019287 0.021106 0.022794 0.024390 0.025864 0.027432 0.028716

LrlgO-199 g 0.137678 0.133844 0.130155 0.126795 0.123366 0.120077 0.116905 0.113835 0.110878 0.108050 u 0,02gg74 0.031025 0.032054 0.033013 0.033888 0.034699 0.035451 0.036124 0.036743 0.037324

Lz200-209 g 0.105298 0.102643 0.100291 0.097838 0.095447 0.093154 0.090945 o.o88809 0.086134 0.084743 U 0.037824 0.038285 0.038883 0.039251 0.039573 0.039856 0.040106 0.040303 0.040478 0.040636

L:210-219 g 0.082822 0.080957 0.079158 0.077408 0.075918 0.074303 0.072724 0.071184 0.069720 0.068298 u 0.040738 0.040810 0.040873 0.040904 0.041092 0.041066 0.041037 0.040981 0.040892 0.040804

Ln220-229 g 0.066905 0.065554 0.064268 0.063008 0.061785 0.060798 0.059652 0.058529 0.057458 0.056415 u 0.0406gO 0.040558 0.040409 0.040266 0.040109 0.039903 0.039905 0.039713 0.039494 0.039276

L.230-239 g 0.055392 0.054085 0.053067 0.052140 0.051418 0.050526 0.049669 0.049029 0.048224 0.047443 U 0.039052 0.038816 0.038568 0.038322 0.038079 0.037809 0.037540 0.037477 0.037214 0.036923

L.240-249 g 0.046679 0.045912 0.045181 0.044474 0.043805 0.043134 0.042664 0.042006 0.041385 0.040783 U 0.036636 0.036359 0.036092 0.035794 0.035509 0.035226 0.034926 0.034643 0.034285 0.034244

L-250-259 g 0.040204 0.039620 0.039040 0.038485 0.037944 0.037428 0.036915 0.036392 0.035894 0.035447 U 0.033970 0.033677 0.033382 0.033096 0.032793 0.032486 0.032080 0.031881 0.031595 0.031341

L=260-269 g 0.034972 0.034510 0.034078 0.033796 0.033369 0.032 i 61 0.032524 0.032109 0.031730 0.029098

0.031524 U 0.031233 0.030965 0.030695 0.030425 0.030133 0.029 68 0.029593 0.029340 0.028810

L-270-279 g 0.031166 0.030807 0.030444 0.030087 0.029731 0.029383 0.029061 0.028719 0.028371 0.028235 U 0.028533 0.028503 0.028242 0.027977 0.027709 0.027451 0.027219 0.026961 0.026691 0.026450

L.280-289 g 0.027917 0.027617 0.027339 0.027060 0.026783 0.026494 0.026177 0.025879 0.025621 0.025556 u 0.026206 0.026158 0.025900 0.025636 0.025403 0.025186. 0.024934 0.024891 0.025621 0.025556

L.290-299 g 0.025290 0.025045 0.024806 0.024575 0.024302 0.024057 0.023833 0.023801 0.023576 0.023347 L:300-300 g 0.023105

300 Atomic Data and Nuclear Data Tables, Vol. 25. No. 4duly lSB0



Ener 'gy = 10.0 eV K=

4.518809 4.871060

25.976817 Number: gerade = 366 ungera tde = 323

1.002471 2.276483 1.571008 3.015351

3.479921 4.428468

4.614987 5.810613

0.406834

1.306385 1.273625

2.200029

4.863133

0.313737

4.144478 0.017763

6.197395

5.061653 0.165879 4.466048 5.802798 2.690902 4.687701 6.268437 3.332062 2.821604 1.900099 5.064005 0.507781 0.546090

5.514497 1.928265

4.396583 3.003742 3.453047 3.834829 2.680150 4.472349 2.061993 4.957630 1.576768 5.324090 1.201322 5.598552 0.913932 5.802377 0.695670 5.952413

0.530759 6.062071 0.406968 6.141039

LZO-g

L.lO-19

L:20-29

t=30-39

L=40-49

L=50-59

Lt60-69

L-70-79

L.ao-a9

L190-gg

L.lOO-109

L.llO-119

L=120-129

L-130-139

L1140-149

L=150-159

Lr160-169

L=170-179

L=lao-la9

L--190-199

L.200-209

L.210-219

L-220-229

L-230-239

L-240-249

L.250-259

L.260-269

L=270-279

L=280-289

L.290-299

L:300-309

L=310-319

L-320-329

l-=330-339 Ln340-349 L=350-359 L.360-365

g ”

5.939195 0.095235 3.853443 0.906035

3.059121 5.202527

:*:t',::: .

0.198939 1.214164 6.2648g3 0.112084

m;; . 4.163gii 1.199695

:%;:z .

1.792886 2.291756

1.352204

5.084765

3.491200

4.944259 0.0805ao 5.692202 0.130634 4.965253 5.708009 3.087006 4.559821 0.299527 3.190044 3.070436

1.757537 5.260294

0.373975 0.700161

5.395120 2.048488

4.294318 3.096928

2.239886 4.752823

2.245989 3.285574 5.286757 5.725087 0.131346 0.024905 0.087945 5.453010 5.608864 3.474063 4.429772 0.606589 3.047435 3.313481 1.615493 5.451932 0.241409 0.850499

5.277383 2.165719 4.193810 3.187735

3.072705 5.985340

2’6265%: . 5.470086 0.204258 0.170621 0.626504 0.038192 5 -929594

5 '550%: . 4.297742 0.906592 2.904370 3.550867 1.474063 5.639019 0.110140 0.997187 5.161297 2.280032 4.095074 3.276213

54-93;90:;; . :%E: . 6.034124 3.078227 0.223165 2.896915 6.058414 1.446178

5.056437 5.280672

0.225417

0.330309

5.445348

4.356836 2.486071

6.187626

6.136766 3.755058 0.212546 3.432173 5.978275 1.870707

4.936205 5.617585 3.613786 2.306064 2.186417 4.657066 0 .-I78894 0.226412 5.758041 1.678590

4.606394 2.810012

%::;43 2.821720 4.358223 2.174249 4.871044

1 .664296 5.258930 1.268704 5.549924 0.965317 5.766398

0.734591 5.926029 0.560155 6.042913 0.429035 6.127274

0.784571 0.230615

0.321908

4.620858 3.325252 6.225485

6.192598

4.416067 0.193320 3.955117 5.892981 2.285541

4.813229 5.946785

3.473357 2.566855 2.043093 4.862966 0.642775 0.388201

5.635477 1.804991

4.500613 2.908125

;:X;o" 2.750151 4.416063

2.117444 4.914944

1.619971 5.291976 1.234562 5.574598 0.939270 5.784662 0.714850 5.939430 0.545262 6.052647 0.417840 6.134272

g ”

B ”

3.758890 0.745774 5.916887 2.385159 0.224733 2.349039 6.133094 1.011721

5.173709 4.935868 3.891471 1.765797 2.473658 4.230265 1.054257 6.173963 6.007772 1.416130

4.823193 2.606088

3.809425 3.528236 2.969656 4.237730 2.292013 4.779485

1.756395 5.189910 1.339767 5.498329 1.019599 5.728155

0.775752 5.897937 0.591214 6.022475 0.452397 6.112555 0.347864 6.177151 0.269346 6.222900 0.210427 6.254893 0.166084 6.276795

0.132574 0.008269 0.113033 0.025920

0.094559 0.031523 0.080579 0.034608 0.068828 0.035936 0.060719 0.037211 0.054495 0.036567 0.049706

0.216817 1.788230 6.202030 0.567104

:-:sB198;: . 4.028423 1.486049 2.617362 4.009138 1.193366 5.999940 6.134868 1.279924 4.934186 2.500150 3.902882 3.446414 3.046058 4.175000

2.353016 4.731761

1.804221 5.153896

g ”

2.329975 4.446203 0.916078 0.060633 5.882148 1.548992

4.713924 2.709354

: ::A,",:: 2.894886 4.298793 2.232431 4.825905

1 .709765 5.224916 1.303768 5.524505 0.992090 5.747566 0.754886 5.912206

0.575463 6.032859 0.440551 6.120037

0.338959 6.182481 0.262736 6.226709

0.205401 6.257481 0.162302 6.278588

0.129663 0.009422 0.110816 0.026609

0.092852 0.031943

0.079251 0.034786 0.067798 0.035986 0.059886 0.037158

0.053853 0.036367 0.049191

g ”

B ”

1.333325 5.821657 6.263401 1.140301 5.046896 2.391489 3.998094 3.362426 3.124103 4.110556

2.415466 4.682697

1.853254 5.116833 1.414687 5.443604 1.076927 5.687524

g ”

8 u

g ”

4.527119

2.007871

0.148161

4.999130

0.001734

1.534656 5.355282 1.168953 5.621803 0.889275 5.819559 0.677008 5.964995 0.516713 6.071188

0.396397 6.147582 0.305804 6.202028

0.237825 6.240395

0.186662 6.266895

t3 ”

2.479381 4.632256

0.376147

1.903526 5.078705

6.160017

1.453638 5.415020 1.106779 5.666271 0.841970 5.852373 0.641236 5.989241 0.490047 6.088560

0.386124

1.955057 5.039482 1.493625 5.385584

6.153904

1.137450 5.644370

0 .a65298 5.836218 0.658871 5.977178 0.502988 6.080018

1.376736 5.471369 1.047877 5.708147

0.624089 0.607411 6.000675 6.011749

0 -464594 6.104822

0.357018 6.171632 0.276233 6.219021

0.215599 6.252208 0.169934 6.274924

0.135498 0.007075 0.114262 0.025167

0.096281 0.031103 0.080788 0.034376

0.069883 0.035865 0.061548 0.037231 0.055148 0.036638 0.050259

0.283311 6.214991

0.366445

0.220925 6.249418

0.173913

6.165926

6.273008

0.138539 0.005829 0.116476 0.024405

0.098074 0.030635

0.083300 0.034153

0.070935 0.035758

:-00;5:;: . 0.055845 0.036726 0.050791 0.035619 0.046899 0.043943 0.040406 0.037484

0.298093 6.206506 0.232032 6.243515 0.182283 6.269026

0.144867 0.003156 0.116468 0.014473 0.100661 0.029641 0.086168 0.033633 0.073164 0.035551 0.064165 0.037268

0.290591 6.210825 0.226400 6.246526 0.178056 6.271086

0.141666 0.004521 0.118867 0.023573 0.098780 0.030169 0.084705 0.033889 0.072052 0.035676

0.063256 0.037255 0.056527 0.036833

0.045582 0.042779 0.039467 0.036669

0.256241 6.230322 0.200516 6.259969 0.158616 6.280269

0.126901 0.010524 w.108697 0.027292 0.091214 0.032305 0.077982 0.034983 0 .o67922 0.036026

0.059101 0.037120 0.053202 0.036404 0.048646

0.249925 6.233802

0.195767 6.262369 0.155034 6.281882

0.124207 0.011602

fy6;:;

0.08g608 0.032678 0.076752 0.035168 0.066957 0.036073

0.243790 6.237160 0.191149 6.264677 0.151546

0.121541 0.012620 0.104557

0.000244

0.028530

0.088053 0.033028 0.075524 0.035305 0.065980 0.036084 0.058718 0.037035 0.051962 0.036211 0.047677

g ” g ” B ” 8 ” g ” I3 ” 8 ” is ” B ” B B

0.118966 0.013579 0.102580 0.029112

0.074342 0.035448 0.065066 0.037248

0.052596 0.036271 0.048153

0.046456 0.043512 0.040112 0.037120

0.051387 0.036142 0.047170 0.051937 0.051312

0.035999 0.035871 0.046716 0.046222 0.043533 0.043125 0.041059 0.040748 0.037958 0.037745

0.044720 0.044325 0.043915 0.042093 0.041731 0.041408 0.038876 0.038608 0.038242

0.046034 0.045162 0.042443 0.039219 g

B

301 Atomic Data and Nuclear Data Tables. Vol. 25. No. 4, Juty 1980

302 GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV

GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs

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Scattering of protons by hydrogen atoms at low energies: Phase shifts and differential cross...

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