МУЛЬТИПОЛЬНЫЕ РЕЗОНАНСЫ

ФОТО- И ЭЛЕКТРОВОЗБУЖДЕНИЯ ЯДЕР

SD- ОБОЛОЧКИ

Н.Г.Гончарова

Particle Core Coupling (PCC) version of the Shell Model

•'

'

(J ), ji, i i

(J ), jA 1 i iJ T C (J 'E'T') (nlj) : J ,T−= ×∑

'

' '

(J ), j'f , f f

(J ), jA 1 f fJ T (J 'E'T') (n 'l' j') : J ,T−= ×∑α

ii

i

SCS

≈∑

Matrix elements of Hamiltonian

ij j c ij ijH (E ' E ) V= + + +ε δ

ijV =

Nuclear photo- and electroexcitations

( ) ( ) ( )4 2

2 2 2ML T4 2

R

q qd e,e 4 F q, tg F q,d q 2q 2

μ μ⎧ ⎫⎛ ⎞ ⎛ ⎞′σ πσ θ⎪ ⎪= ω + + ω⎜ ⎟ ⎜ ⎟⎨ ⎬⎜ ⎟ ⎜ ⎟Ω η ⎪ ⎪⎝ ⎠ ⎝ ⎠⎩ ⎭

( ) ( ) { } ( )max maxJ J2 212 el mag 2 2

T i f J i f J i EJ MJJ 1 J 1

F q 2J 1 J T (q) J J T (q) J F F−

= =

= + + = +∑ ∑

Summed squared form factors: electroexcitation of sd-shell nuclei

1ħω resonances in sd-shell nuclei: E1, M2, E3, M4, E5, M6

Photopoint : 1

excq E 0.1 0.2Fmω −= ≡ ≈ ÷

Spectroscopy of pickup reactions on 18O

E1 in 18O at photopoint

2/52/3

2/32/3

2/12/3

111121

dpdpsp

→→→

2/52/5

2/32/5

2/72/5

112111

fdpdfd

→→→

U.Kneissl ea // Nucl.Phys.A272,125 (1976)

18O(γ,n)

Spectroscopy of pickup reactions on 22Ne

E1 in 22Ne at photopoint

22Ne(γ,n)V.V.Varlamov,M.E.StepanovMSU-INP,1999

ii

i

SCS

≈∑

E1 in 24Mg at photopoint

15.00 20.00 25.00 30.00 35.000.00

0.10

0.20

0.30

0.40 a

15.00 20.00 25.00 30.00 35.000.0

10.0

20.0

30.0 b

F2 × 102

σ, mb

Exp: Ishkhanov B.S. ea., Nucl. Phys.A186 (1972) 438

P.M. Endt, Nucl.Phys.A521(1990)1

E1 in 26Mg at photopointF2 × 102

Exp (c): (γ, n)+(γ, n+p)+(γ, 2n) Fultz S.C. et al., Phys. Rev. C4 (1971) 149

σ, mb

E, MeV

10.00 20.00 30.00 40.000.00

0.40

0.80a

10.00 20.00 30.00 40.000.0

20.0

40.0c

27Al+γ → 26Al+n

Exp: M.N.Thompson et al // Nucl. Phys. 64 (1965)486

Динамические деформации при фоторасщеплении 27Al

• 27Al+γ → 26Al+n 27Al+γ → 26Mg+p

H. Röpke, P.M.Endt // Nucl. Phys. A632(1998)173.

Спектроскопия реакции подхвата32S(d,3He)31P

Спектроскопия реакции 32S(d,3He)31P;Е*- энергии возбуждения ядра 31P

J.Vernotte et al,Nucl.Phys.A655(1999)415

E1 excitations 32S

Exp: B.S.ISHKHANOV et al,2002.PCC version of SM

Спектроскопия реакции подхвата34S(p,d)33S

34S – photoneutron reaction

E1 excitation of 48Ca

Excitation and disintegration of 48Ca(isospin factors)

48Ca( , n)γ

O’Keefe G.J. , Thompson M.N. et al // Nucl.Phys.A469(1987) 239

48Ca( ,p)γ

O’Keefe G.J. , Thompson M.N. et al // Nucl.Phys.A469(1987) 239

E1 resonances in (e.e’)Spin- and orbital currents interference in E1 sd-shell form factors

For E1 transitions

maxima of C1 form factors (a) are near minima of E1 form factors(b)

1/2 3/21 1( 1)= + = +⇒ +j L j LL L

F2(q) for E1 transitions

MJmax excitations

max

2 222 2( ) exp( )

2∼ J

MJ f J ib q

F J O q J C q= × −

max2J

qb

=

MJmax (stretched states)

Spin current contributions only

M6 in sd-shell nuclei : 28Si

E, MeV

q = 1.8 Fm-1

S.Yen,ea,Phys.Lett.B289, 22(1992):6- T=1 at 14.32 MeV

Endt P.M. Nucl. Phys. A 310 (1978)

M6 in sd-shell nuclei : 32S

Exp.: Clausen B.L et al , Phys.Rev.C48, 1632(1993).

Exp

q = 1.8 Fm-1

M6 in Ca-40

M2 resonances

Spin- an orbital currents in M2 excitations

Nuclear Orbital M2 CurrentOrbital M2 TWIST Mode: Orbital current has oppositesignes in the upper and lower semispheres.The current vanishes at

Z=0

( ) ( )( )2

2 2 22 =

⎡ ⎤Υ Ω ×∇⎣ ⎦∼Jmag i

j i jeT j qrq

(e,e’) excitation ~Spin+orbital(twist)

modes

(p,p’) excitations –SPIN part onlyComparison of (e,e’) and (p,p’) reveals

ORBITAL TWIST M2-

M2 in 32S(e,e’)

Experiment: S-DALINAC (Emax=14 MeV) E, MeV

F2 × 105

8.00 12.00 16.00 20.000.000.501.001.502.002.50

S-320.7 g free

8.00 12.00 16.00 20.000.0

4.0

8.0

12.0

16.0S-32

F2 × 106

q = 0.6 fm-1

Spin and orbital currents in M2 32S

E, MeV

F

q-dependence of M2 peaks

Summary• In the PCC version of SM distributions of the ”hole”

among the (A-1) nuclei states are taken into account in microscopic description of multipole resonances in sd-shell nuclei using spectroscopy of pick-up reactions.

• The energy spread of final nuclei states is the main origin of the multipole resonances fragmentation in open shell nuclei. Comparison of PCC SM results with experimental data on MR confirms the validity of this approach for a range of momentum transfer from “photopoint” up to q≈2 Fm-1.

• The assumption that some very valuable information on MR in excited deformed nucleus is embedded in direct reactions spectroscopy data proved to be right.