The structure of giant resonances in calcium and titanium isotopes.

N.G.Goncharova, Iu.A.Skorodumina

Skobelzyn Institute of Nuclear Physics,

Moscow State University

Origins of multipole resonances fragmentation?

E1 in Titanium Isotopes

Particle Core Coupling Shell Model (PCC SM )

'

'

( ),,

( ),1( ' ' ') ( ) : ,J j

i i iJ j

i iAJ T C J E T nlj J T

'

' '

( ), ',

( ),1( ' ' ') ( ' ' ') : ,J j

f f fJ j

A f fJ T J E T n l j J T

ii

i

SÑ

S

Matrix elements of Hamiltonian

( ' )ij j c ij ijH E E V

(1) (2)

' ' ' '' '' ''1 2( )( ) : ( )( )

ij f f

f f

V J V J

J ET j J V J E T j J

int 12 1 2 0 1 1 2 0 1 2 1 1 2 1 2( ) ( ) ( )V r g r r f f g g

48 47pT(p,d) Ti;E 35MeV

46 45pT(p,d) Ti;E 35MeV

P.Plauger, E.Kashy, Nucl.Phys.A152(1970)609

ii

i

SÑ

S

50 49pTi(p,d) Ti; E 45 MeV

ii

i

SÑ

S

Number of basic configurations

E1 form factors

, ,

' ',,,

' '

2 2 1 ( );

( ) ( , , , , ).

T T T

i f

fi

T

J J Jf f T TM i i T f TM i i TM f i

i j j

J T jJT jJTM f i i f i f i f i f

J T

J T M B J TM j O j J Z j j

Z j j C f J J j j T T

20Г 2 ( )i i imk P k S

1/2 1/21 1, (2 1) (2 1) 0

i f

elE SN CM i f i T f T f f E i iF q f f J T TM T T M J T T J T

228

( ) ( )Td F q

46TiIsospin factors in excitation and decay

48TiIsospin factors in excitation and decay

50TiIsospin factors in excitation and decay

E1 form factors at photopoint in 46Ti

R.E.Pywell, M.N.Thompson ea ,Nucl.Phys. A318 (1979)461

E1 form factors at photopoint in 48Ti

R.Sutton, M.N.Thompson et al , Nucl.Phys. A 339(1980)125

48Ti(γ,n)

E1 form factors in 50Ti

50Ti(γ,n)

R.E.Pywell, M.N.Thompson R.A.Hicks, Nucl.Phys. A325(1979).116

Spectroscopy of 40Ca(d,t) at Ep=52 MeV

P. Doll, G.J. Wagner, K.T. Knopfle, Nucl.Phys. A263(1976) 210

E1 in 40 Ca

A.Veyssiere et al., Nucl. Phys.A227(1972)513

M6 in Ca-40q = 1.8 Fm-1

5/2 7/21d 1f

The maximal energies of projectiles in the pick-up reactions and occupation of 1d5/2 subshell

Spectroscopy of 48Ca

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

Mean weighted energies for T< and T>

branches and isospin splitting

Bull.RAS,Physics,75(2011)1540-1543Bull.RAS,Physics,76(2012)1085-1088

SUMMARY

1.The calculations of the E1 strengths in calcium and titanium isotopes have shown that one of the main origins of resonances’ fragmentation is the energy spread of final nuclei states. This factor could be taken into account in PCCSM.

• 2.For the realistic description of the nuclei disintegration due to interactions with electromagnetic fields spectroscopic information on direct reactions should be obtained with energy of projectiles at least on 15 MeV higher than the maximum energy of the photon.

The structure of pigmy resonances = a problem

T. Hartmann et al, Phys. Rev. Lett.,.85 (2000) 27448Ca(e,e ')

Behavior of form factors E1