Extracting information from charge exchange reactions the tools we have--what we need Sam Austin 28 September 2009, ECT

Transcription

1 Extracting information from charge exchange reactions the tools we have--what we need Sam Austin 28 September 2009, ECT Contexts: Type Ia (Thermonuclear) Supernovae: SN1006 Arizona Petroglyph Core Collapse Supernovae SN 1987a Evolution of neutron star crusts in binary systems very n-rich nuclei Double Beta decay Nuclear Structure Electron capture, Beta decay rates for A 60 Rates for a large range of A up to 120 and beyond, NSF PHY & PHY (JINA)

2 NSCL Charge Exchange Program Interests Electron capture rates (SN) Structure (light nuclei) Double beta decay Experiments Stable nuclei: (t, 3 He)-- NSCL ( 3 He,t) RCNP Unstable nuclei (Inverse) ( 7 Li, 7 Be), (p,n) Description Phenomenology Theory 2

3 Needed Information for SN Electron Capture Why is it a challenge? Weak transition strengths Electron-capture (Gamow-Teller) -Decay (Gamow-Teller & Fermi) Summary (Juodagalvis, et al., arxiv: ) Stable nuclei A 65 (200 nuclei) SM effective interactions, good but inadequate Masses to A = (250 nuclei) SM calculations not yet possible SMMC + RPA Heavier nuclei FD (Fermi Dirac) +RPA (2200 nuclei) Unstable Nuclei Experiments difficult Complication-stellar environment Finite (high) T, density Transitions from excited states Experiments impossible So many nuclei and BESIDES 3

4 Meeting the challenge a beginning Philosophy Not possible to measure all or most of rates needed for astrophysics or some other applications. Concentrate on validating the theoretical calculations. But pay attention to crucial, accessible cases. Develop a phenomenological procedure for describing data (t, 3 He) measurements--nscl: 115 MeV/A, ΔE 250 kev ( 3 He, t) Osaka: 140 MeV/A, ΔE = kev Quantify the accuracy of the procedure What is needed, theoretically and experimentally, to improve the results Measurement emphasis on the lighter nuclei A <65 : Compare with Shell Model--two different residual interactions. Find strong sensitivity to interaction for some nuclei Testing model calculations for Double Beta Decay what approach

5 Charge-exchange reactions and the Unit Cross Section No Q-value restrictions (unlike -decay) Single step above E 100 MeV/A, simple descriptions are possible Stable nuclei: Probes include: (p,n), (n,p), (d, 2 He), ( 3 He,t), (t, 3 He), ( 7 Li, 7 Be),( +, o ), ( -, o ) Unstable nuclei: inverse kinematics--the nucleus of interest is the beam-- ( 7 Li, 7 Be), (d, 2 He)(?), and (p, n) seem feasible d 2 The crucial equations: ( q 0) KN D J B( GT ) d ˆ unit cross section K= Kinematic factor N D = Distortion factor = DW (q=0)/ PW (q=0) J = Volume integral of GT interaction ˆ KN D J 2 d d ( q B( GT ) 0) 5

6 (t, 3 He) at 115 MeV/A and ( 3 He,t) at 140 MeV/A Distortions & re-scattering not minimal, but small enough to ensure predominant single-step mechanism Central t-matrix--love Franey Isospin t-matrix Love Franey Іt στ І 2 Іt tta τ І 2 Spin-flip Isospin-flip transitions are near maximal. Non-spin-flip isospin-flip transitions are strongly suppressed Franey & Love, PRC 31, 488,

7 Unit cross section 109 A Measure cross sections for transitions with B(GT) known from β decay. Extrapolate to q = 0 Determine for ( 3 He, t) and (t, 3 He) reactions with known large B(GT) Find that unit cross section has simple dependence on mass number A From cross section for any transition can determine B(GT) from the curve. Zegers et al. PRL 99, (2007) G. Perdikakis et al. to be published A.L. Cole et al. PRC 74, (2007) Zegers et al. PRC 77, (2007) Zegers et al. PRC 74, (2006) General approach of Taddeucci et al. NPA 469, 125 (1987) for (p,n), but consider also the effects of the Tensor interaction in more detail 7

8 The Tensor Force Problem GT Excitation > 1 + can have L = 0, 2 amplitudes Central Force L = 0, 2 add incoherently, L= 2 small, a few percent Tensor force L = 0, 2 can interfere, much larger effects. Cross section at q = 0 may contain L = 2 contributions and give incorrect B(GT). Can t evaluate effect without detailed wave functions. But can t you find L=0 part by multipole expansion? NO! σ tot aσ L=0 + bσ L= 2 MD may not yield a reliable result Example: 37 Cl(p,n) 37 Ar at 120 MeV, E x = 0, 3/2 - Full-sd-shell wave functions. Austin, Anantaraman, Love, PRL 73, 30 (1994)

9 Size of Effect Plot σ(q=0) /B(GT) vs B (GT) 37 Cl(p,n) 37 Ar 120 MeV For L=0 amplitudes (best (inaccessible) case), < 5% deviations Larger deviations for smaller B(GT) For L= 0 + 2, some states may have x 2 deviations Outliers Different effective interactions, different states have large effects Tensor + C

10 64 Zn (t, 3 He) 64 Cu Hitt et al. PRC 80, (2009) The situation for ( 3 He, t) and (t, 3 He) 115 MeV/A, GXPF1A wave functions, first states E x < 6 MeV. Calculate σ (DWBA), treat as data (assumed unit σ). Rel. Syst. Error = B( GT ) DWBA B( GT ) B( GT ) SM SM 1 2 There are Outliers σ(rel. Syst. Err.) ln[b(gt)] For B(GT) = 10-2 σ (RSE )= 18% % 1 3% Similar studies 24,26 Mg, 58 Ni Zegers et al. Y. Fujita, et al. PRC 75, (2007)

11 Similar Results for (p, n ) and (n, p) Sasano et al. PRC 79, (2009) M. Sasano, Private Comm. Similar, somewhat smaller spread, outlying points

12 Unit Cross Section From Theory ˆ theory DWBA q 0 B Use DWA code FOLD of Cook and Carr Love-Franey nucleon- nucleon (C + SO + Tensor) Interaction is double folded over transition densities taken from variational Monte Carlo (Pieper - Wiringa) 3 He-- > t GT transition strength is ± (Chou, Warburton, Brown) Exchange treated in zero-range approximation (ignored for tensor) One body transition densities from Shell-Model or normal modes calculations B calculated with same wave functions L= 2 contributions estimated by turning off the tensor interaction

13 Experiment vs. Theory-PRC 74, (2006) EXPERIMENT THEORY σ GT σ GT 1.3 x EXPT σ/σ FIT EXPT Experiment tight correlation after one L=2 correction Theory on average ~ 1.3 x Experiment

14 Cause of Discrepancy? No Clear answer Density dependence of interaction Love-Franey not accurate Zero-range approximation for exchange Distorting potentials not well known true, but doesn t seem to be 30% effect

15 How Well Do Shell Model Calculations Describe The Data 64 Zn(t, 3 He) 64 Cu Hitt, et al. Howard et al It depends! Differences for 64 Zn strongly affect electron capture rates in Supernovae calculated using a code developed by S. Gupta : A. D. Becerril-Reyes, S. Gupta, H. Schatz, K.-L. Kratz, and P. Möller, PoS NIC-IX, 075 (2006)

16 Nature of capture process: Electron energy midpoint depends on ρ Width depends on T Electron Capture Rates for 64 ZN Low ρ, T, only low E x states contribute Increasing either ρ or T brings in higher E x. But low E x states contribute most strongly for given B(GT) because of larger phase space. Present case: 25 M sun star in various stages of Si burning Mainly low E x important so both theories underestimate rate, KB3G more.

17 Shell Model Calculations NSCL CE group + A. Cole, Kalamazoo College Have undertaken large basis shell model calculations for pf shell Different effective interactions try to determine sensitivity trends Hope to provide a guide to experiment-what s important to do. UseNuShellX (Rae, Horoi, Brown) W. D. M. Rae, Can run many nuclei without truncations KB3G updated version of one used for rate-set by Martinez-Pinedo et al. A. Poves et al., Nucl. Phys. A694, 157 (2001). GXPF1A M. Honma et al., Eur. Phys. J. A 25, 499 (2005) Calculate weak rates using a code developed by S. Gupta A. D. Becerril-Reyes, S. Gupta, H. Schatz, K.-L. Kratz, and P. Möller, PoS NIC-IX, 075 (2006) Examine two more cases: 45 Sc, 51 V 17

18 EC RATES FOR 45 Sc Data: 45 Sc(n, p) x100 Crucial to describe Low E x data accurately 18

19 EC RATES FOR 51 V Data 51 V(n,p) and 1 V(d, 2 He) Data with low resolution ((n, p)) in this case) can help validate theory, but are not necessarily good for producing rates. 19

20 Double Beta Decay--Comments Two Neutrino Decay Measure GT strength to intermediate virtual states from Initial and final states Sometimes find a single low lying state of intermediate nucleus is sufficient to explain lifetime Constrains the nature of higher lying contributions: are contributions in phase, are there strong transitions from both directions Advantage we have an observable : τ 1/2 Zero Neutrino Decay We are trying to measure something, no fixed observable has major effect on on how we proceed

21 Constraining the Description of 2β0ν Decays Situation Many states of high excitation and various multipolarities are involved Impossible to measure properties of most of them Cannot constrain their overall effects as in 2ν decay Minimum requirement on theories-my view Theories must reproduce Charge-Exchange measurements with sufficient accuracy to make their farther reaching predictions (m ν ) credible Can this be done? I doubt if reaction theory is up to precise comparisons Next a brief discussion of why.

22 Comments Needs Theoretical Homework (p, n)/(n, p) A simpler reaction mechanism ( 3 He,t)/(t, 3 He) Better resolution. Well defined systematics Most items below apply to both A reaction code that includes exchange for complex projectiles, (d, 2 He), ( 3 He, t), (t, 3 He), ( 7 Li, 7 Be) Re-evaluation of the effective interaction and its density dependence Is Love Franey still good enough? Does proportionality fail in (n, p) direction for neutron rich nuclei (Amos, Faessler, Rodin Phys. Rev. C 76, (2007) )? A procedure to evaluate cross sections for reactions leading to states in the continuum. Presently assume such states are weakly bound. Sakai presented one case where this is done. If multipole decompositions are to be done, need a way to choose contributing orbitals as a function of excitation: Can the SMMC provide this information?

23 Take Home Lessons For Experimenters-I The effects of the tensor force are sometimes large Little independent evidence on accuracy of tensor force Normalization to small B(GT) is uncertain--if choose the wrong state could be x 2 errors Normalizing ( 3 He, t) or (p, n) to the ratio of Fermi and GT strength can be inaccurate. Density dependence is larger for Fermi transitions--need to understand its effects much better. For 48 Ca(p, n) adding exchange to tensor interaction increases the IAS cross section by 15% at 120 MeV (R.G.T.Zegers, P.C.) There are unresolved uncertainties for certain nuclei, 13 C, 15 N, 39 K, for example. Best practice: use average curves such as those shown here.

24 Homework For Experimenters A To Do list Develop techniques for doing charge exchange with unstable beams. Validate the SMMC + RPA and FD + RPA techniques used for predictions of Electron Capture strength in heavier nuclei. Push for development of techniques for description of charge exchange with complex projectiles take advantage of the good resolution they can provide. Obtain a systematic approach to optical models for all reactions High statistics experiments are time consuming. Develop collaborations at several facilities to achieve a sufficient systematics.

25 Experiment Y. Fujita, M. Fujiwara, H. Ejiri, T. Adachi et al. (Osaka/RCNP), H. Sakai, S. Shimoura, et al. (Univ. of Tokyo), Y. Shimbara (NSCL, now Niigata U.) D. Frekers et al. (Univ. of Münster), M. Harakeh (KVI) Jenna Deaven, Carol Guess, Rhiannon Meharchand, Du Nguyen, Amanda Prinke, LeShawna Uher Wes Hitt (MSU Students) S. M. Austin, D. Bazin, A. Cole[now Kalamazoo], A. Gade, B.M. Sherrill, K. Starosta, D. Weisshaar, Remco Zegers(MSU), G. Perikakis Theory M. Horoi (CMU), B.A. Brown (MSU) G. Colo, S. Fracasso (Milano) Astrophysics E. Brown, D. Chamulak (MSU) S. Gupta (MSU, now LANL) Those involved NSF PHY & PHY (JINA) 25