RPA CORRECTION TO THE OPTICAL

POTENTIAL

Guillaume Blanchon, Marc Dupuis, Hugo Arellanoand Nicole Vinh Mau.

CEA, DAM, DIF

CNR*11, 22/09/11, Prague.

◮ Parametrized potentials are very useful but onlyin the range of the fit and they are mostly local.

◮ Long time quest for more microscopic potentials◮ From NN realistic interaction: nuclear matter, FRPA

S. Waldecker, arXiv:1105.4257v1 (2011).◮ From NN effective interaction: Skyrme or Gogny force

◮ Microscopic potentials are non-local and energy dependent◮ Need for tools to determine bound states and continuum states◮ Need for reaction tools able to deal with non locality.

◮ Microscopy can be a guide line for new parametrized non-localpotential Perey & Buck, NP 32, 353 (1962), W. Dickhoff, PRC

82, 054306 (2010).

Microscopic N-nucleus optical potential

NA POTENTIAL

MICROSCOPICA+1 nucleons

INTERACTION NN

2−body

◮ Nucleon scattering off stable nuclei

◮ Nuclear structure 7−→ Nuclear reaction◮ Elastic scattering◮ RPA (double closed-shell, spherical symmetry)◮ Gogny force / G-matrix (Melbourne, Santiago)

Nuclear matter approach

Proton elastic scattering off 208Pb (M. Dupuis, et al., PRC 73, 014605

(2006).)

◮ MelbourneG-matrix

◮ DWBA98(J. Raynal)

◮ No parameter

Good agreement with experiment at high incident energy⇒ Lack of absorption below 60 MeV.

Nuclear structure approach

“Optical potential for low-energy neutrons”,

(N. Vinh Mau, A. Bouyssy. NPA 257 (1976) 189-220.)

Coupling to collective states of the target nucleus

◮ Green’s functions formalism.

◮ Second order double counting issue.

◮ Absorption at small incident energy

Ingredients:

◮ D1S Gogny force.

◮ RPA, spherical symmetry (Gogny, Decharge).

V. Bernard and N.V. Giai, NPA 327, 397 (1979)

F. Osterfeld, et al. PRC 23, 179 (1981).

Integro-differential Schrodinger equation

◮ Non-local and energy dependent optical potential.

◮ Integro-differential Schrodinger equation,

[

d2

dr2+

l(l + 1)

r2− k2

]

fjl(r) +

∫

dr ′Ujl(r , r′)fjl(r

′) = 0

No localization of the potential

◮ We use a modified version of DWBA98 code for continuumwave functions. (J. Raynal. computer code DWBA98, 1998,

(NEA 1209/05).)

◮ We determine bound states for a non-local potential incoordinate space (Important to get the right asymtpoticbehavior of the wave function).

First strategy: G-Matrix / RPA-D1S

MELBOURNESANTIAGO

G−MATRIXDWBA98 CODEVBHF

CROSS SECTION

SCHRODINGER NL

RAYNAL

First strategy: G-Matrix / RPA-D1S

RPA+VVBHFMELBOURNESANTIAGO

G−MATRIX

DOUBLE COUNTING

WITH G−MATRIX

DWBA98 CODE

NUCLEAR STRUCTURE

RPA/D1SDECHARGE & GOGNY

INTERMEDIATE

DISTORTED

WAVE

CORRECTIONRPA CROSS SECTION

SCHRODINGER NL

RAYNAL

Second strategy: HF + RPA-D1S

RPA+VHFV

D1S

RPA/D1SDECHARGE & GOGNY

HF/D1S

INTERMEDIATEDISTORTED

WAVE

RPACORRECTION

CROSS SECTION

SCHRODINGER NL

RAYNALDWBA98 CODE

Imaginary part of VRPA

Coupling to 3− states with Eexc < 30 MeV.

Proton scattering off 208Pb,ImVRPA.

◮ Einc= 40 MeV

◮ Eexc < 30 MeV → 115states.

◮ Intermediate → Plane wave

◮ V jlRPA(r , r)

3−j,l j,lVRPA

jl

Imaginary part of VRPA with incident energy

VRPA: Coupling to the first 3− Eexc =3.4 MeV

Proton scattering off 208Pb for sev-eral incident energies.

W (R , s) =∑

lj

2j + 1

4πImV lj

RPA(r , r′)

with R =1

2(r + r ′) and s = r − r ′

→ Absorption coming from cou-pling to a given RPA state de-creases as the incident energy in-creases

Non-locality of the imaginary part of VRPA

VRPA: Coupling to the first 3− Eexc =3.4 MeV

◮ Surface picked contribution: collectivity

◮ Gaussian like non-locality → Perey & Buck

Cross Section: VBHF+VRPA neutron-40Ca @ 40 MeV

◮ n+40Ca @ 30 MeVContribution from differentexcitations of the target.

◮ Cross section: Melbourne Gmatrix

◮ n+40Ca @ 40 MeV◮ Melbourne + RPA/D1S

Reaction cross section n/p off 40Ca

10 15 20 25 30 35 40E

lab (MeV)

0

500

1000

1500

σ R

(mb)

hf+rpaKD

20 25 30 35 40E

lab (MeV)

600

700

800

900

1000

σ R

(mb)

hf+rpaKD

◮ HF+RPA with D1S (Intermediate plane wave)

◮ Comparison with reaction cross section obtained withKoning-Delaroche (KD) global potential.

◮ Distorted waves are expected to lead to an enhancement of theabsorption

◮ Coupled channels calculation gives less absorption considering onlyinelastic couplings. They emphasize the contribution of thedeuteron pickup channel. G. Nobre et al., PRL 105, 202502 (2010).

◮ Summary

◮ RPA correction deals with part of the observed absorption butother channels would be needed: deuteron channel, chargeexchange.

◮ We develop tools to get bound as well as scattering statesusing any non-local potential.

◮ Use of intermediate distorted waves is expected to lead too anenhancement of absorption.

◮ Perspectives

◮ A systematic study of: VRPA is in progress.◮ Microscopic potentials can guide new global parametrizations.◮ Extension to QRPA nuclei.◮ Add of damping widths in the propagators.◮ Coupled channels with non-local potentials (deformed target).