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Microscopic description of E1 resonance in light nuclei
Goncharova N.G, Tretyakova T. Yu, Fedorov N.A. SINP MSU

JUNE 27, 2015

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Plan

1 2 3 4 5 6

Introduction Silicon isotopes Model of particle-core coupling (PCC) Resonance excitation schemes Form factors of E 1 resonance Results

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Introduction

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Silicon isotopes

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Properties of silicon isotopes

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Properties of silicon isotopes

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Model of particle-core coupling (PCC)

Within the PCC version, the wave functions for the ground and excited states of the nucleus being considered can be represented as the following expansions: |Jf Tf = |Ji Ti = where |(J E T )( function.
A-1) J f T jf

|(J E T )(

A-1)

в (nf lf jf ) : Jf Tf в (ni li ji ) : Ji T
i

CiJ

T ji

|(J E T )(

A-1)

is core wave function, and |(nf lf jf ) -particle wave

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Model of particle-core coupling (PCC)
|Jf Tf = |Ji Ti =
J · The co efficients f



JTj f

f

|(J E T )

(A-1)

в (nf lf jf ) : Jf Tf , в (ni li ji ) : Ji Ti ,

(1) (2)

CiJ
Tj

T ji

|(J E T )(

A-1)

arise upon the diagonalization of the Hamiltonian in the basis of the configurations · Co efficients CiJ T ji were estimated with the aid of exp erimental data on the spectroscopy of direct nucleon-pickup reactions: Si CiJ T ji , where Si is the spectroscopic factor of the S
k

f

reaction that leads to the excitation of the (J E T ) level of the final-state nucleus (A - 1) · Sk is the sum of spectroscopic factors of the states with (J , T ) · Photonuclear cross-section in E1 resonance area can b e estimated by form factor calculation in photopoint q = Eexc . F
2 EJ

=

1 ^ el | Jf Tf ||T1 (q = )||Ji Ti |2 . 2Ji + 1

(3)
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E 1 resonance excitation in

28

Si

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E 1 resonance excitation in

30

Si

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Basis

· Basis parameters

Nucleus,|T | Basis dimension Reaction
· Spectroscopy for · for
30

Si 25 28 Si(p,d) Tp = 34MeV
28

28

Si T = 1 38 30 Si(p,d) Tp = 27MeV

30

Si T = 2 13 30 Si(p,d) Tp = 27MeV

30

Si: R. L. Kozub Phys. Rev. 172 (1968) 1078­1094

Si: 17. R.C. Haight et al Nucl. Phys. A241 (1975) 275

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Form factors of E 1 in

28

Si

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Results for

28

Si

Experiment: R.E. Pywell et al. Phys.Rev.C 27 (1983) p960, reaction 28 Si( ,n)27 Si
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Form factors of E 1 in

30

Si

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Results for

30

Si

Experiment: R.E. Pywell et al. Phys.Rev.C 27 (1983) p960, reaction 30 Si( ,n)29 Si
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Thank you for your attention!

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Properties of silicon isotopes

A 26 27 28 29 30 31 32 33

J

P

Ebin /A MeV 7924.707 8124.337 8447.744 8448.635 8520.654 8458.291 8481.468 8361.059 ± ± ± ± ± ± ± ± 0.004 0.005 0.000 0.001 0.001 0.001 0.009 0.021

0+ 5/2+ 0+ 1/2+ 0+ 3/2+ 0+ 3/2+

Abundance or T1/2 2.229 s 4.15 s 92.223 ± 0.019 % 4.685 ± 0.008 % 3.092 ± 0.011% 157.3 m 153 y 6.1 s

Decay Mo des 100% 100%

- 100% - 100% - 100%

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Properties of silicon isotopes

Separation energies for one (Bn ), two (B2n ) neutrons and one proton (Bp ). Data from AME2012
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Deformation

The deformation parameter calculations in HF for silicon isotopes. The solid line­resuls from J.-P. Delaroche et al, Phys. Rev. C 81 (2010) 014303, dashed line­S.Goriley, At. Data and Nucl. Data Tables 77

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Deformation

A 26 27 28 29 30 32 34 36 38 Data

2 (B(E2)) 0.444 ± 0.022 0.407 ± 0.007

2 (Qmom ) 0.097 ± 0.006 (g.s.) -0.352 ± 0.076 (2+)

2 -calc

Charge radius

-0.366 0.179 -0.23

0.316 ± 0.007 +0.094 ± 0.118 (2+) 0.345 ± 0.031 +0.293 ± 0.05 (2+) 0.179 ± 0.036 0.259 ± 0.042 0.249 ± 0.048 from CDFE: http://cdfe.sinp.msu.ru

3.1224 ± 0.0024 3.1176 ± 0.0052 3.1336 ± 0.004

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Decay width calculation
We can estimate the
i j

by formula (4) (4)

2 ij = 2Cw ij kij P (lj )Tij

where Cw is the Wigner's width, -coefficient from (1), kij = 2mparticle (Ei - Ef - E c
sep

)

, Tij = Tf T3f Tparticle T3

particle

|Ti T3i 2 , (5)

P (lj )-penetrability of angular momentum barrier. Cw =
2 2rchannel

3( c )2 mparticle c

2 2E i

MeV 2 fm2 = MeV fm2 MeV
i

(6)

fi

1+

2arctg (

)

=

8 2 Fi2 Ei
i 2 2

(7) (8)
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ij =

fi ij 1 (E - Ei )2 +


Spectroscopy of

28

Si

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Spectroscopy of

30

Si

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