Probing nuclear potential with

reactions

Krzysztof Rusek Heavy Ion Laboratory, University of Warsaw,

www.slcj.uw.edu.plThe Andrzej Soltan Institute for Nuclear Studies,

www.ipj.gov.pl

Going out of the valley of stability

Can we use the standard form of effective nucleus-nucleus potential?

Magic numbers are no longer magic

Nuclear halos

Importance of three-body forces

Granulation of nuclear matter

etc.

Effective nucleus-nucleus potential

V = Vo + iW

Vo :

W = 0.5 Vo

G.R. Satchler, W.G. Love, Phys.Rep. 55 (1979)183

Elastic scattering

Deviation from Rutherford c.s. at very forward angles

6Li + 208Pb

6He + 208Pb

Y. Kucuk, N. Keeley PRC 79 067601 (2009)

Elastic scattering

Structure effects important!

L. Acosta et al. EPJ A in print

↑

↓

Complete fusion

R

V

Complete fusion

Supression above the Coulomb barrierL.R. Gasques et al. PRC79 (2009) 034605

Complete fusion

Enhancement below the Coulomb barrier

S.M. Lukyanov et al. PLB 670 (2009) 321

↑

The method (continuum-discretized coupled-channels)

[T + εg.s. – E + <ψg.s.(r)I V(r,R) Iψg.s.(r)>] χel(R) = <ψg.s.(r)IV(r,R)Iψinel.(r)> χinel(R)

... . . . . . . . . . . . . . . . . . . . . . .

Φ(r,R) = ψg.s.(r)χel(R) + ψ1exc(r)χinel(R) + ..

The method at work

Structure of 6He is ”reflected” in elastic scattering close to the barrier

K. R. PRC72, 037603↓

The concept of DPP(dynamic polarization potential)

local, L-dependent DPPs, many methods to derive L-independent DPP.

If the method is working well, results (σel ) should be close to CDCC

V = Vo + iW + DPP

Method 1: inversion S → VIP method of R.S. MackintoshReview of IP method: V.I. Kukulin and R.S.Mackintosh, J. Phys. G: Nucl. Part. Review of IP method: V.I. Kukulin and R.S.Mackintosh, J. Phys. G: Nucl. Part. Phys. Phys. 3030, R1 (2004) , R1 (2004)

Method 2: „trivially equivalent potential”

[T + Vo + i W + DPP] χel(R) = E χel(R)

χel(R) from CDCC calculations

Case 1 – 4He + 238U

Solid, dashed – CDCC, Dotted – OM+DPP

Strong repulsion at the surface is due to nuclear interactions (absorption)

Case 1 – 4He + 238U

Solid, dashed – CC, Dotted – OM+DPP

Strong repulsion at the surface is due to nuclear interactions (absorption)

Exp. data of Budzanowski et al., PL 11 (1964) 74

Solid – CDCC, dashed – OM+DPP

Case 2 – 7Li + 208Pb

Coupling with unbound states generates similar DPP as with bound state

Exp. data Keeley et al., NPA 571 (1994) 326

Case 3 – 6He + 208Pb

Long range attraction due to dipole polarizability

Contiunnum dominated by L=1 states

Exp. data A. Sanchez-Benitez et al., NPA803 (2008) 30

Similar tendency – repulsion at the surface and long range attraction reflecting dipole couplings with the continuum

Conclusion

DPPreal = V1 df/dR + V2 g(R)

DPPimag = W1 df/dR + W2 g(R)

f(R) = [1+exp(R-R0,i)/a1]

g(R) = [1+exp(R-R0,i)/a2]

Parametrization

V1 /W1

V2 /W2

Ro,i a1 a2

real 6.5 0.20 10.3 0.80 6.0

imag 6.5 0.35 9.8 0.50 3.0

V = Vo + i W + DPP

Explanation of all the effects observed for el. scatt. and fusion.

Consequences

Prediction for fusion barrier distribution – shifts it to higher energies and make broader

Consequences

K. Zerva et al., PRC80(2009)017601

6Li + 28Si

Recipe

V = Vo + iW + DPP

Vo – from densities

W – a half of V0

DPP – coupling with direct

reaction channels

Parametrization

V1 /W1 V2 /W2 Ro,i a1 a2

real 6.5 0.20 10.3 0.80 6.0

imag 6.5 0.35 9.8 0.50 3.0

V1 /W1 V2 /W2 Ro,i a1 a2

real 6.5 0.05 10.05 0.50 3.0

imag 0.0 6.0 10.30 - 0.40

V1 /W1 V2 /W2 Ro,i a1 a2

real 6.5 0.18 8.2 0.55 2.8

imag 0.3 0.18 10.8 0.55 3.0

α + 238U

7Li + 208Pb

6He + 208Pb

CYCLOTRON

PET QCC H E M I S T R Y

QC

Pro

d.

Pro

d.

CYCLOTRON

GDR

EXPERIMENTAL HALL

SEPARATORICARE

BIOLOGY

CUDAC

K = 160

EAGLE

Energies 2 ÷10 MeV/A

Ions 10B ÷ 40Ar

Potential from transfer reaction analysis

Probability: potential a + A

+ structure

+ potential b + B

a + A

B + b

10B + 7Li → 8Be + 9Be

A.T. Rudchik et al. PRC 79 054609 (2009)

The method (continuum-discretized coupled-channels)

[T + εi – E + <ψi(r)IV(r,R)Iψi(r)>] χi(R) =

<ψi(r)IV(r,R)Iψk(r)> χk(R)

Φ(r,R) = ψ1(r)χ1(R) + ψ2(r)χ2(R) + …..

prof. G. Rawitscher

Input parameters

- Structure of the projectile(wave functions)

- Fragment – target interactions

No free parameters