Recent developments in the Lorentz. Transform (LIT)) method

Transcription

1 Recent developments in the Lorentz Integral Transform (LIT)) method 10 th anniversary Response Functions from Integral Transforms with a Lorentz Kernel V. D. Efros, W. Leidemann and G. Orlandini, Phys. Lett. B338, 130 (1994) UNIVERSITY of TRENTO Winfried Leidemann G. O. P.h.D. students: Sonia Bacca Sofia Quaglioni Mario A. Marchisio Collaborators: Hartmuth Arenhövel ( Mainz) Nir Barnea (Jerusalem) Victor Efros (Moscow) Doron Gazit (Jerusalem) Ed Tomusiak (Victoria) G. Orlandini Microscopic Nuclear Structure Theory - Oct. 13, 2004

2 Outline of the talk Review of the LIT method for inclusive reactions Review of the LIT method for exclusive reactions Results on reactions with electromagnetic probes on: 3-body systems (e,e') 4-body system (e, e' p), (g, p) 4-body system (total photoabsorption) 6-body systems (total photoabsorption) 7-body system (total photoabsorption) Conclusions and outlook

3 the LIT is a method for ab initio calculations of reactions to continuum it is general enough to be applied to strong as well e.m. reactions the applications so far have been for e.m. reactions What is the aim of ab initio calculations of e.m. reactions?

4 Ab initio calculation means: the framework of NR quantum mechanics explicit degrees of freedom in the H are A nucleons the inputs are the nuclear potential and the (possibly consistent!) excitation operator relevant to the reaction

5 Remark on: why e.m. discrepancies between e.m. cross sections from ab initio calculations and experiments can mean: either insufficient knowledge of the potential or H and excitation operator are inconsistent or relativistic effects may be important or other degrees of freedom ( implicit in V, but generating new e.m. operators)

6 Remark on : why continuum we hope to see resonances and collective modes generated by microscopic treatment of the A-body dynamics

7 The LIT method Generalities: from few (many) body structure ab initio i.e. the framework is NR quantum mechanics the explicit degrees of freedom are A nucleons dynamics the inputs are the nuclear potential and the excitation operator relevant to the reaction does not calculate continuum states does calculate matrix elements (or combinations of ME) to continuum states cross sections

8 The LIT method Generalities (cont): needs only a good method for bound state calculations applies both to inclusive reactions (straightforward!) and to exclusive ones has been benchmarked in 2- and 3-body systems where continuum states can be calculated directly [Lapiana&Leidemann NPA677(2000)423] [Golak et al. NPA707(2002)365]

9 The LIT in practice: For inclusive reactions one needs to know ò steps: 1. Solve for many ω 0 and fixed Γ

10 2. Calculate Γ ω 0 for a Theorem based on closure 3. Invert transform

11 The theorem: Closure = 1

12 For exclusive reactions one needs to know steps: 1. Solve for many ω 0 and fixed Γ same as before!

13 2. Calculate overlap Γ E 0 3. Invert transform and find F(E) for a Theorem based on closure 4. Calculate matrix element of interest

14 The theorem: (I) difficult part

15 The theorem: (II)

16 The theorem: (III) Use closure = 1

17 main point of the LIT : Schrödinger-like equation with a source Theorem: The behavior solution is unique and has bound state asymptotic one can apply bound state methods

18 To calculate reactions with LIT one needs: 1. the potential V 2. a good method to solve bound states The following results are obtained with 1. various V NN and V NNN 2. Hyperspherical Harmonics expansions (CHH, EIHH)

19 RESULTS

20 3 - body

21 3-Body total electrodisintegration LONGITUDINAL RESPONSE Role of 3-Nucleon force low q AV18 AV18 + UIX CHH Efros-Leidemann-Orlandini Tomusiak PRC69(2004) Exp: O: Dow 1988 Δ: Marchand 1985

22 3-Body total electrodisintegration LONGITUDINAL RESPONSE Role of 3-Nucleon force high q AV18 AV18 + UIX CHH Exp: O: Dow 1988 Δ: Marchand 1985

23 how big is the potential model effect?

24 How big is the effect of an exact treatment of the continuum (FSI)? 4 He MTI/III

25 Total electrodisintegration of 3 He Role of 3-Nucleon force LONGITUDINAL RESPONSE low energy AV18 AV18 + UIX CHH Exp: Retzlaff 1994

26 3-Body total electrodisintegration Frame dependence AV18 + UIX CHH

27 4 - body

28 Total photodisintegration of 4 He Data: (γ, n) Berman et al '80 + (γ, p) Feldman et al '90 Is there a giant dipole resonance in 4 He? PRL 78,4015(1997)

29 4 3 He(g, p) He nm 4 He(g, p) 3 H

30 4 3 He(g, p) He nm PWIA AGS AGS

31 4 He(g, p) 3 H

32 4-Body exclusive: 4 He (g, n) 3 He S.Quaglioni et al. PRC69(2004) Data: LUND PRELIMINARY! CHH PWA MT I-III

33 An excellent method to solve bound states: the Effective Interaction in Hyperspherical Harmonics method (EIHH) N.Barnea, W.Leidemann, G.O. PRC61(2000) similar idea as for the No Core Shell Model method i.e. use of Effective Interaction applied to H.H. instead of H.O. no parameter fast convergence can be applied to A>4

34 EIHH with realistic forces: convergence AV18 + UIX N. Barnea et al: nuc-th/

35 4 He total photodisintegration with realistic potential Data: (γ, n) Berman et al '80 + (γ, p) Feldman et al '90 Preliminary!

36 4-Body exclusive: 4 He(e,e p) 3 H Longitudinal ( MT potential) Parallel Kinematics: Ducret et al. NP A556 (1993) 373 p m MeV/c PWIA+AS +AS+FSI+FSI + CHH

37 6-Body total photodisintegration Appearance of collective motion 6 Li EIHH soft mode 6 He classical GT mode S.Bacca et al. PRL89(2002)052502

38 comparison with experiment 6 Li 6 He

39 7-Body total photodisintegration S.Bacca et al. nucl-th '75 '75

40 Conclusions the LIT represents a break through on the way from ab initio NUCLEAR STRUCTURE ab initio NUCLEAR REACTIONS also for A>4 only bound state technique is needed

41 We have seen examples where in reactions one can test : interaction semirealistic versus realistic V NN, 3N force effects limits of NR QM frame dependence approximations PWA... microscopic origin of collectivity soft mode and giant resonance

42 outlook A lot of work for a lot of years to come, both for theory and for experiment! Theory: increasing A (8-9???) various other reactions (e.w., incl, excl.) realistic interactions also for A>4 application of the LIT to hadronic reactions Experiment: more data at low energy higher precision data

43 References: 3-body inclusive Longitudinal response PRC 69 (2004) body exclusive reactions 4-body exclusive reactions PRC 69 (2004) body total photodisintegration 6-body total photodisintegration PRL 89 (2002) , PRC 69 (2004) body total photodisintegration 7-body total photodisintegration nucl-th EIHH EIHH PRC 61 (2000) ; NPA 693 (2001) 565; nucl-th