Study on -A Reaction Cross Sections within CRPAJeong-Yeon LEE and Yeong-Duk KIMSejong University, KOREA

I. Why -A interactions? : play an important role in various astrophysical processes, dynamics of core-collapse supernovae and supernova-nucleosynthesis, with the detection of neutrinos from SN1987A. : interesting tools to study weak interaction, the limits of the standard model, and nuclear structure. Though neutral-current scattering is important in astrophysics, experimental works concentrate on charged-current reactions, since outgoing charged leptons are more easily detected. Scattering off nuclei like 12C and 16O (i.e., the main constituents of scintillator and water Cerenkov detectors) has been the object of many investigations. Longstanding problems concerning discrepancy between theoretical and experimental results for 12C(, -)12N* could not be solved satisfactorily.

Motivation of a new study of charged-current -A reactions, including calculations of cross sections for nuclei of experimental interests.

II. Continuum RPARandom phase approximation (RPA) - A nucleus is excited primarily through ph excitation. - Interaction between p and h produces correlations between ph pairs, which play an important role in determining characteristics of energy spectrum. Giant resonance (GR) states : Collective states described as superpositions of many 1p-1h configurations. well describe the positions & strengths, but not the widths of GR. ( states are treated as discrete ones even in continuum.)

Continuum RPA

Nuclear response in continuum - ph correlations. - damping (absorption) effects. - continuum boundary condition.

Quite successful in explaining

Giant resonances : Hadronic inelastic scattering (Lee et al., JNST S2, 770(2002), JKPS 36, 323 (2000), 36, 13 (2000) & 33, 388 (1998)) Electronic inelastic scattering ( Kyum, Ph. D. thesis, 1996.) -excitations by charge exchange reactions : (p,n), (3He,t) (Udagawa et al., PLB 245, 1 (1990), PRC 49, 3162 (1994) )

III. PurposesCalculations of cross sections for -A reactions, 12C(l , l - )12N*, 16O(l , l - )16F*, using the continuum RPA. Comparison with the experimental data. Comparison with cross sections for reactions by other probes.

IV. Charge-exchange -A scattering Charged-current reactions

l + X(Z,A) l - + X(Z+1,A), l = e, e : coming from decay-at-rest of +. : coming from decay-in-flight of +.

Assumption : Target is a spherical nucleus with J = 0+ . -A reaction cross section

G : Weak interaction coupling constant. c : Cabibbo angle. F(Z,E) : Fermi function. X

MJ(), LJ(), JJmag(), JJel() : Coulomb, longitudinal, transverse magnetic, transverse electric multipole operators.

V. Nuclear strength function in Continuum RPAStrength function

i, f : Quantum numbers of initial and final states. : Generic many-body operator.

Assumption :Target is a spherical nucleus with J = 0+.

Source function

Yp : Spin-angle wave function of particle p.

h : Hole wave function of h (=time reversal state of h).( | | : Integrals are carried over only spin-angle variables.

~~

Greens function

: Excitation energy of system ( >0 for forward amplitude,

How can we obtain ?? Introduce !!!

ph : Correlated source function. G0 : Free Greens function without Vph.

Inhomogeneous coupled-channels integral equation.

Use Lanczos method to solve ! (Whitehead et al., Adv. Nucl. Phys. 9, 123 (1977).

S : Damping(spreading) process.

S : Direct knockout (particle emission) process.

( p : Distorted wave function of knocked-out p against residual nucleus)

VI. Applications Apply to 12C(l , l - )12N *, 16O(l , l - )16F*

Hh = Th+Uh (Uh : Mean field real potential of Woods-Saxon type)

Hp = Tp+Up (Up : Optical potential of Woods-Saxon type )

Vph (r1,r2)= Vph(|r1-r2|) [W + BP +M Px + H PPx ] (P ,Px: Spin, coordinate exchange operators) Assume : - Vph is a local 2-body operator. - We use -interaction approximation.

Vph (r1,r2)= Vp (r1-r2) [a +bP ] , a= W+M, b=B+H

Cross section for 12C(, -)12N*

VII. SummaryWe study charge exchange -A scattering reactions, 12C(l , l - )12N *, 16O(l , l - )16F*, in a self-consistent manner within Continuum RPA. Numerical calculations for cross sections will be done up to higher order of multipole transitions and be compared with the experimental data. Further works - Comparison of -A and -N scattering cross sections. - Comparison with cross sections for the reactions by other probes.