1.Description of correlations in mean-field and beyond mean-field methods

1.Description of correlations in mean-field and beyond mean-field

methods

Spatial structure of Cooper pairs in HFB approach

N.Pillet(1), N.Sandulescu(4), P.Schuck(3)

2.Nuclear excitations in plasmas

G.Gosselin(1), V.Méot(1), N.Pillet(1)

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Jeunots 2008, February 4-6 (2008), Saclay

Variational multiparticle-multihole configuration mixing method

N.Pillet(1), J.-F.Berger(1), E.Caurier(2), H.Goutte(1),

N.Vinh Mau(3), F.Chappert(1)

(1) SPN,CEA-Bruyères-le-Châtel (3) IPN, Orsay

(2) IPHC, Strasbourg (4) IPNE, Bucharest

Variational multiparticle-multihole configuration mixing

Motivations:

• Towards a unified description of correlations in the context of beyond mean- field method {essentially Pairing + RPA + particle-vibration coupling}

• Conservation of particle numbers + enforced Pauli principle

• Description on the same footing of even-even, odd and odd-odd nuclei

• Description of both ground states and excited states

Description of correlations in mean field and beyond mean field methods

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Formalism:

• Trial wave function: Superposition of Slater determinants corresponding to mpmh excitations built upon a given state of HF type



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h2p2

h2p2

h1p1

h1p1h0p0 AAA

N

1ii 0a

m

1)kl(lkaawith an

d

+ + + …

• Variational principle

o Optimized single particle states:

o Mixing coefficients:



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o Functional: )(H)(

0A

)(*

A)(H)(HA

0)(

*i

),(G),(h

Simultaneous solution of both equations (iterative):self-consistent procedure and renormalization of the

HF field

ˆwith

(*) N.Pillet, J-F.Berger and E.Caurier, under submission to PRC.

N.Pillet, N.Sandulescu, Nguyen Van Giai and J-F.Berger, Phys.Rev.C71, 044306 (2005).

Current study:



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Pairing correlations and link with projection on particle

number methods-Applications to Sn isotope ground states(*)

Structure of correlated wave functions

Correlation energy (MeV) Only configurations

with excited pairs

D1S Gogny force

ij 2

A)j,i(T



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Effect of correlations on single particle spectra

Charge radii

Future studies:

• Link with RPA – How to simulate RPA calculation with mp-mh method?

Which one-body density should be used?

• Description of light exotic nuclei (B, Li, Be, C, N, O, F) – PhD Proposal

Application of the mp-mh method to odd and odd-odd nuclei

Effect of general correlations on single particle spectra

Applications to island of inversionRe-fit of Gogny interaction (D2)?

Need for experimental data on masses, spins, parities… towards drip lines



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(*) N. Pillet, N. Sandulescu and P. Schuck, Phys. Rev. C76, 024310 (2007).

• Method: HFB with D1S Gogny interaction

• Spherical nuclei: O, Ca, Ni, Sn, Pb isotopic chains

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Brody-Moshinsky transformation K(R,r) (R: center of mass, r: relative coordinates)

Two-body correlated wave function (J=0):

)(cosP)()r()r(K)1j2(41

)r,r(K 12ll

2l2n1l1nlj2n1n

lj1n2n0S21

0;lnln0;nlNl)(cosP)R2()2/r()l2

1l2()(

K)1j2(41

)r,R(K

1211lNlnNl

nl2/1

1

l

1j1l2n1n

1j1l

1n2n10S

2rr

R 21

21 rrr

and

Size of Cooper pairs:

2/122

2/124

dsindr,r,RKr

dsindr,r,RKr)R(

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Strong coupling behavior of Cooper pairs on the surface of superfluid nuclei

Probability Distribution

222 )r,R(KRr)r,R(P

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Future study: Generalization to deformed nuclei where the parity mixing is expected to be stronger + nucleon pair transfer

Nuclear excitations in plasmas

Photon absorption

NEEC

(nuclear excitation by electron capture)

NEET

(nuclear excitation by electronic transition)

Inelastic electron scattering

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Main excitation processes

Corresponding de-excitation processes Photon emission

spontaneous+ stimulated

IC

(internal conversion)

BIC

(bound internal conversion)

(*) P.Morel, V.Méot, G.Gosselin, D.Gogny and W.Younes, Phys.Rev.A69, 063414 (2004).

(*) G. Gosselin, V. Méot and P. Morel, Phys.Rev.C76, 044611 (2007).(*) G. Gosselin, V. Méot and P. Morel, Phys.Rev.C70, 064603 (2004).

•Photon absorption, NEET and NEEC mechanisms (*):

First order perturbation theory Fermi golden rule

Method for transition rate calculation:

•Inelastic electron scattering: (under development)

Second order perturbation theory

PWBA, WKB, DWBA (radial transition matrix element)

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201Hgm

Two level model

Photon+NEEC/IC+NEET/BIC

(thermodynamical equilibrium)

(*) V.Méot, J.Aupiais, P.Morel, G.Gosselin, F.Gobet, J.N.Scheurer and M.Tarisien, Phys. Rev. C75, 064306 (2007).

201Hg

g.s.0 keV

1.56 keV

26.27 keV

81ns(*)3/2-

1/2-

5/2- 630ps

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Lifetime of first 201Hgm

Future: inclusion of inelastic electron scattering

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Future

• Variational multiparticle-multihole configuration mixing method

• Spatial structure of Cooper pairs

• Nuclear excitations in plasmas

Link with RPA

Study of light nuclei- PhD proposal

Test and possible re-fit of Gogny interaction (D2)

Generalization to deformed nuclei + pair transfer

Inclusion of inelastic electron scattering

Κ2(R,r) in Sn isotopes and Parity mixing effect

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Shell effects + Parity mixing effects

Probability Distribution 222 )r,R(KRr)r,R(P

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dr)r,R(Kr

)r,R(Kr)r,R(W 22

22

Future study: Generalization to deformed nuclei where the parity mixing is expected to be stronger + nucleon pair transfer

Documents

1.Description of correlations in mean-field and beyond mean-field methods