QRPA based calculations for neutrino scattering and electroweak - PowerPoint PPT Presentation

QRPA based calculations for neutrino scattering and electroweak excitations of nuclei. Arturo R. Samana in collaboration with Francisco Krmpotic, Alejandro Mariano, Cesar Barbero – UNLP -Argentina Carlos A. Bertulani -Texas A&M University – Commerce-USA Nils Paar – University of Zagreb – Croatia 08/11/2015 (NUCFACT2015) – Rio de Janeiro- Br - 2015

Outline ▪ Motivation Neutrino physics and Nuclear Structure. ▪ Weak-Nuclear interaction Formalism Nuclear Models SM, RPA, QRPA, PQRPA, RQRPA ▪ Results on 12C, 56Fe and systematic calculations ▪ Summary

Motivation KARMEN (1983-2005) KARMEN, no oscillation signal LSND (1993-2005) LSND experiment observes excesses of events for both the  and  oscillation.      ( ) ( ) ( , ) J n E E J dE   f f A. Samana , F. Krmpotic , A. Mariano,R. Zukanovich Funchal/ Phys. Lett B642(2006)100

Motivation ( 10 -40 cm 2 )  -nucleus cross section are important to * Increase probability oscillations. * Confidence level region is diminished constrain parameters in neutrino by difference in  e between oscillations.         PQRPA and CRPA, PLB (2005) 100 e e

Supernovae Neutrinos – Signal Detection Neutrino flux  E ( ) Number of target nuclei Efficiency  Interaction cross section        ( ) ( ) ( ) N N F E E E dE     ev t ( ) F E  0 SNO LVD            p n e d p p e e e LVD      12 12 C N e e      12 12 C B e Super-K e      56 56 Fe Co e      16 16 e O F e e      56 56 Fe Mn e      16 16 O N e e BOREXino e

Weak – nuclear interaction Charg rged ed Current ent 12 C 12 N Neutr utral al Curren ent 12 C 12 C *        * ( , ) ( 1 , 1 ) A Z N A Z N e e        * ( , ) ( 1 , 1 ) A Z N A Z N e e (i )O’Connell, Donelly & Walecka, PR6,719 (1972) (ii) Kuramoto etal. NPA 512, 711 (1990) ALL ARE EQUIVALENTS. (iii) Luyten etal. NP41,236 (1963) (iv) Krmpotic etal. PRC71, 044319(2005). 6

Weak – nuclear interaction Reaction: Weak hamiltonian:   G           i k r ( ) H r J l e ( , ) ( 1 , ) Z A Z A l   W l 2 Neutrino- nucleus cross section (Fermi’s Golden Rule):  1 p E      l l ( , ) ( 1 , ) (cos ) (| |, ) E J F Z E d T k J   l f l f 2  1 p l :Lepton momentum, E l : Lepton energy, F(Z+1,E): Fermi function Transition amplitude  2 1 G    2       (| |, ) | | | | k J J M H J M L   b b   f f f W i i 2 1 2 1 J J s s M M M M i i  l f i f i     Nuclear Matrix Element , Lepton traces L b   i k r || || , J J e J   f i      Transfer momentum, with k = | k| ž. ( , ), . | | . k k k r k r Ø Hadronic current (non-relativistic)

Weak – nuclear interaction Non-relativistic approximation of hadronic current 2    2 Nuclear coupling constant   g  g   FNS effect:   2 2   k  =850 MeV Transfer momentum, with k = | k| ž. Elementary Operators :

Weak – nuclear interaction L ; L M L ; 0 Lepton Traces ☺ For natural parity states with  =(-) J ,i.e., 0 + , 1 - , 2 + , 3 - …. ☺ For unnatural parity states with  =(-) J+1 ,i.e., 0 - , 1 + ,2 - , 3 + …. (i) deForest Jr.& Walecka, Adv.Phys15, 1(1966) (ii) Kuramoto etal. NPA 512, 711 (1990) (iii) Luyten etal. NP41,236 (1963)(  -capture) (iv) Krmpotic etal. PRC71, 044319(2005).  all are equivalents.

Nuclear Structure Models (i) M odels with microscopical (ii) M odels describing overall nucler formalism with detailed nuclear properties statistically where the structure, solves the microscopic parameters are adjusted to exp. quantum-mechanical Schrodinger or data, no nuclear wave funct., Dirac equation, provides nuclear polynomial or algebraic express. wave functions and (g.s.-shape E sp , J  , log (ft), t 1/2 … ) Examples: Examples: Shell Model ( Martinez et al. PRL83, 4502(1999) ) Fermi Gas Model, Gross Theory of b -decay (GTBD) RPA models Self-Consistent Skyrme-HFB+QRPA Takahashi etal. PTP41,1470 (1969) New exponential law for b  ..... ( Engel etal. PRC60, 014302(1999) ) QRPA, Projected QRPA ( Zhang etal. PRC73,014304(2006) ) t 1/2 ( Kar etal., astro-ph/06034517(2006) ) (Krmpotic etal. PLB319(1993)393.) Relativistic QRPA (N. Paar et al., Phys. Rev. C 69, 054303 (2004)) Density Functional+Finite Fermi Syst. ( Borzov etal. PRC62, 035501 (2000) ) 10

Nuclear Structure Models SHELL MODEL → accurate in description of the ground state wave functions, description of high-lying states necessitates a large model space which is problematic to treat numerically Different interactions in various mass regions employed, only lower mass nuclei can be studied The interacting shell model is the method of choice for weak interactions ( b -decay,  -capture, e - -capture) Why? Pauli blocking/ unblocking example: Now consider neutrino and t hese orbits are filled anti-neutrino capture      A B e e OK! “ Hartree-Fock configuration” HYPERSIMPLE SCHEME 11

Nuclear Structure Models Nuclear Structure Models : SM      A C e e X NO! requires too NO! much energy!! Pauli blocked! But, if  = + + c +... Some weak processes (usually p  n ) blocked because neutron orbits already occupied. But configuration mixing, even a little, can unblock by creating holes for the new neutron to go into. thus: Weak processes sensitive to configuration mixing For example: ''... the total GT strength for 56Fe in the OK! complete pf shell involving 7 413 488 J=0+ configurations (this corresponds to an m-scheme dimension of 501 HYPERSIMPLE SCHEME million). E. Kolbe et al., PHYSICAL REVIEW C, VOLUME 60, 052801 12

Nuclear Structure Models QRPA: Quasiparticle Random Phase Approximation       2 2 ( )( ) 0 , e u v u v t t t t t t t PQRPA: Projected QRPA Particle number is conserved exactly . Krmpotic etal. PLB319(1993)393. 13

Nuclear Structure Models RQRPA: Relativistic Quasiparticle Random Phase * Approximation ,       2 2 ( )( ) 0 e u v u v t t t t t t t * N. Paar et al., Phys. Rev. C 69, 054303 (2004)

QRPA/PQRPA in 12 C  Neutrino Scattering (NS)       ( , ) ( 1 , ) Z A Z A l l  Anti - neutrino Scattering (AS)       ( , ) ( 1 , ) Z A Z A l l  Muon Capture (MC) rate        ( , ) ( 1 , ) Z A Z A   Beta decay        ( 1 , ) ( , ) ( ) Z A Z A e e e 15

QRPA/PQRPA in 12 C Volpe etal , PRC 62 (2000) ` `difficulties in choosing the g.s. of 12N because the lowest state is not the most collective one” ph-channel parameters from systematic study GT resonances, F.K.&S.S. NPA 572, 329(1994) ph = v pair , v t ph = v s ph /0.6 P (I) : v s ph =27, v t ph =64 P(II): v s 1p - 1h 2p - 2h 3p - 3h 16

QRPA/PQRPA in 12 C ( 10 -42 cm 2 ) 1p - 1h 2p - 2h 3p - 3h CRPA, Kolbe etal., PRC71, 044319(2005). Projection Procedure is Important! EPT, Mintz, PRC25,1671(1982). PQRPA, Krmpotic etal., PRC71, 044319 Krmpotic etal. PRC71, 044319(2005). (2005). Exp, LSND coll., PRC55, 2078(1997). 17

Summary QRPA/PQRPA in 12 C 18

Summary QRPA/PQRPA in 12 C 19

Summary QRPA/PQRPA/RQRPA in 12 C 20

CRPA/PQRPA in 12 C ( 10 -40 cm 2 ) * Increase probability oscillations.  -nucleus cross section are important to * Confidence level region is diminished constrain parameters in neutrino by difference in  e between oscillations. PQRPA and CRPA,         A.Samana,F. Krmpotic,A. Marianoc,R. Zukanovich e e Funchal PLB (2005) 100

Summary QRPA/PQRPA/RQRPA in 12 C 22

Summary RQRPA in 12 C 23

Summary RQRPA in 12 C Inclusive 12 C( ν , e − ) 12 N cross-section σ e − ( E ν )(in units of 10 − 39 cm2) plotted as a function of the incident neutrino energy E ν , evaluated in RQRPA with different configuration spaces. These cross sections are plotted as functions of the incident neutrino energy with different cut-off of the E 2 qp quasiparticle energy as it is explained in the text. The left and right panels show the cross section evaluated with S 20, and S 30 s.p. spaces. The last cross section shows that the convergence of the calculation is achieved up to 600 MeV of incident neutrino energy. Left and right panels show, respectively, the cross sections σ e − ( E ν ), and σ e + ( E ˜ ν ) (in units of 10 -39 cm 2 ) evaluated in RQRPA for S 20, and S 30 s.p. spaces with the cutoff E 2 qp = 500 MeV, and different maximal values of J ± , with J going from 1 up to 14 for neutrinos, and from 1 up to 11 for antineutrinos. 24