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Study on ν -A Reaction Cross Sections within CRPA

Study on ν -A Reaction Cross Sections within CRPA. Jeong-Yeon LEE and Yeong-Duk KIM Sejong University, KOREA. I. Why ν -A interactions?.

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Study on ν -A Reaction Cross Sections within CRPA

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  1. Study on ν-A Reaction Cross Sections within CRPA Jeong-Yeon LEE and Yeong-Duk KIM Sejong University, KOREA

  2. I. Why ν-A interactions? • ν : play an important role in various astrophysical processes, dynamics of core-collapse supernovae and supernova-nucleosynthesis, with the detection of neutrinos from SN1987A. • ν : interesting tools to study weak interaction, the limits of the standard model, and nuclear structure. • Though neutral-current νscattering is important in astrophysics, experimental works concentrate on charged-current ν 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(νµ,µ-)12N* ⇒could not be solved satisfactorily. ⇒ Motivation of a new study of charged-current ν-Areactions, including calculations of cross sections for nuclei of experimental interests.

  3. II. Continuum RPA • Random 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.)

  4. 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.) • Δ-excitations by charge exchange reactions : (p,n), (3He,t) (Udagawa et al., PLB 245, 1 (1990), PRC 49, 3162 (1994) )

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

  6. l - εf εi θ νl IV. Charge-exchange ν-A scattering X Charged-current reactions νl +X(Z,A) ⇒l -+ X(Z+1,A), l = e, µ νe : coming from decay-at-rest of µ+. νµ : coming from decay-in-flight of π+. Assumption : Target is a spherical nucleus with Jπ = 0+ . ν-A reaction cross section G : Weak interaction coupling constant. θc : Cabibbo angle. F(Z’,E) : Fermi function.

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

  8. V. Nuclear strength function in Continuum RPA • Strength function • i, f : Quantum numbers of initial and final states. • : Generic many-body operator. Assumption :Target is a spherical nucleus with Jπ = 0+.

  9. Source function • Yp : Spin-angle wave function of particle p. • Φh : Hole wave function of h (=time reversal state of h). • ( | | › : Integrals are carried over only spin-angle variables. ~ ~

  10. Green’s function • ω : Excitation energy of system (ω >0 for forward amplitude, ω <0 for backward amplitude) • Hh : Hamiltonian of hole nucleus • Hp (=Tp +Up ): Hamiltonian of excited particle p (Up=Vp+iWp , Wp: deals with damping effects of particle going into more complicated nuclear states) • Vph: Residual interaction (responsible for ph correlations)

  11. • How can we obtain ?? ⇒ Introduce !!! Λph : Correlated source function. G0 : Free Green’s function without Vph. ⇒Inhomogeneous coupled-channels integral equation.

  12. ⇒ Use Lanczos method to solve ! (Whitehead et al., Adv. Nucl. Phys. 9, 123 (1977). S↓: Damping(spreading) process. S↑ : Direct knockout (particle emission) process. (χp : Distorted wave function of knocked-out p against residual nucleus)

  13. VI. Applications • Apply to 12C(νl , l -)12N *, 16O(νl , 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 + BPσ+M Px + H PσPx ] (Pσ ,Px: Spin, coordinate exchange operators) Assume : - Vphis a local 2-body operator. - We useδ-interaction approximation. ⇒ Vph(r1,r2)= Vp δ(r1-r2) [a +bPσ ] , a= W+M, b=B+H

  14. Cross section for 12C(νµ,µ-)12N*

  15. VII. Summary • We study charge exchange ν-A scattering reactions, 12C(νl , l -)12N *, 16O(νl , 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 ν-A and ν-N scattering cross sections. - Comparison with cross sections for the reactions by other probes.

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