Neutrino reactions on two-nucleon system and core-collapse supernova Shota Nasu(Osaka.U) Collaborators: T. Sato (Osaka.U),K. Sumiyoshi(Numazu Coll.Tech.), S. Nakamura (JLab),F. Myhrer (USC),K.Kubodera (USC) I would like to talk on neutrino reaction on the two nucleon system and core-collapse supernova. Those people are the collaborators.

In this work: neutrino production reaction in two-nucleon system Introduction: neutrino reactions in core-collapse supernovae Absorption, production and scattering reactions Electron captures Elastic scattering Pair creation and annihilation Nucleon Bremsstrahlung S. Bruenn (1985) Neutrino absorption: heating mechanism (shock wave revival -> delayed explosion) production: cooling mechanism (proto-neutron star to neutron star, source of neutrinos) Existence of light elements (d,t,3He) K. Sumiyoshi and G. Röpke, (2008) A. Arcones et al. (2008) Neutrino absorption reaction in light elements ( for heating ) page 1 ----------------------------------------------------------------------------- The neutrino scattering, production and absorption reactions play an important role at the various stage of the core-collapse supernova evolution. In the present simulation of the super-nova explortion,typically those reactions are taken into account. Here A is He, Carbon, Oxygen and so on. In this here the neutrino absorptions act as the heating mechanism, which helps to revival of the stalled shock-wave. On the other hand the neutrino productions act as the cooling mechanism which helps transferring the proto-neutron star to neutron star, and the emitted neutrinos are the source of heating mechanism. Recently those authors have shown that there can be a quite amount of light elements, deuteron and triton, helium3 at various stage of supernova-evolution. This motivated us to study possible role of neutrino absorption reactions on those light element in the heating region of SN explosion. In this talk I will report on our effort to extend our previous nu-d work by nakamura-san for neutrino production reaction in two-nucleon system to complete the analysis of whole weak reactions in two-nucleon system. ---------------------------------------------------------------------------- : S. X. Nakamura et al.(2009) : E. O’Connor et al., (2007), A. Arcones et al., (2008) In this work: neutrino production reaction in two-nucleon system (for cooling)

Motivation: Neutrino production in two nucleon collision Modified URCA processes : Neutrino bremsstrahlung : Crucial for cooling mechanism Friman and Maxwell (1979) One-pion-exchange Hanhalt et al.(2001) Low Energy Theorem deuteron in final state : EFT: deuteron as dibaryon Ando, Kubodera (2006) Those works can be used only low energy region. page 2 ---------------------------------------------------------------------------- So far, it is considered that those of the neutrino production reactions on two nucleon play crucial role for the cooling of the proto neutron star and neutron star. First, the NN going to NN e nu_e processes are so-called Modified URCA process Second, the NN going to NN nu nubar is called neutrino bremsstrahlung. The first processes are the charged current reaction and The second is theneutral current reaction. The theoretical evaluation of those lepton production processes have been done using one-pion exchange model with plane wave nucleon scattering state or using Low energy theory which is valid only very low energy region. In the deuteron bound process, The nn -> d e nu , was studied from dibaryon effective field theory. Now all results from those works can be used only at very low energy. Our obfective is to reinvestigate all possible semileptonic process of the two nucleon system for the SN simulation, which can be used away from very threshold region. today I will talk on the study of the nn going to d e nu process. Objective : Analysis of neutrino production reactions on two-nucleon system for SN simulations Today’s talk : process

Formalism Standard Nuclear Physics Approach (SNPA) Weak Hamiltonian: Nuclear currents: page 3 --------------------------------------------------------------------------- To investigate the low energy semileptonic process, we start form the effective weak Hamiltonian of the standard model for charged current and neutral current. We employ the well established so called standard nuclear physics approach where we calculate the amplitude using nuclear wave function and nuclear current. We did not used heavy baryon chiral perturbation theory since we need to evaluate the reaction amplitude up to around 100MeV region. As for nuclear weak current including meson exchange current, we used a model which is developed for the analysis of SNO data. ---------------------------------------------------------------------------- exchange currents + excited exchange currents model of nuclear current used to analyze nu-d for SNO data

Neutrino emissivity Charged current process : emitted neutrino energy S.W.Bruenn(1985) T.A.Thompson et al.(2000)　etc. : emitted neutrino energy : Fermi-Dirac distribution function page 4 ---------------------------------------------------------------------------- For the numerical simulations of SN evolution, magnitude of neutrino production is usualy expressed by neutrino emissivity denoted by Q. Q is esseitially emitted neutrino energy times transistion probability with Fermi-Dirac distribution of initial nucleon and also possible Pauli Blocking factor. Here M is the matrix element of effective Hamiltonian in the previous slide. I will focus Q in my following talk.

Examine the simple case emissivity for nucleon non-degenerate limit for lepton Examine the simple case → keep only dominant 1S0(nn) -> 3S1(d) Gamov-Teller transition : n-n kinetic energy : Neutron density Strong E-dependence of |M|  large 1S0 scattering length page 5 ---------------------------------------------------------------------------- We consider the charged current reaction nn->d e+ nu_e. As an example, we study the non-degenerate limit of the emissivity. The Fermi-Dirac distribution function is treated as an non-degenerate limit. At first, we examine the emissivity keeping only the dominant 1S0 to 3S1 gamov teller transition. In this case the Q can be simply calculated by evaluating the following integral. Here M is essentialy overlap integral of scattering and deuteron wave function. One often use a low energy limit of the nuclear matrix element which is energy independent, however as can be seen in the figure, which is the square of the matrix element as a function of kinetic energy of intial state, the matrix element strongly depends on kinetic energy becuase of the large nn 1S0 scattering length. therfore, Even at low temperature, K_n to the power of 6.5 appearing in the simple formula of Q enhances the higher energy contribution and it shows the importance of taking into acount the energy-dependence of the matrix element. Energy dependence of Even at low temperature.. The facter enhances the high energy contribution

OPE model, approx. E-independent |M| Full result of emissivity IA+EXC nuclear currents, Including higher partial waves OPE model, approx. E-independent |M| T.A.Thompson et al. (2000) etc. page 6 ---------------------------------------------------------------------------- Here is the result. The red line in the figure shows the emissivity for the nn->d e nu reaction. Here we take into account impulse and exchange current and NN partial wave till we get convergence. In low temperature, the T-dependence is rather flat instead of naive expectation of power law behavior. For comparison we plot the bremsthruhlung process in blue line. This is from Tompson which is calculated using One-pion-exchange mechansim and constant nuclear matrix element. It can be seen that the emissivity of nn going to deuteron reaction is much larger than that of blems in the low temperature region. At the temperature 1MeV, Qnn-d is about Qnn-nn times 10 to the power of 5.

Summary near future plan Analysis of neutrino emissivity ・ examine validity of using low energy approximation ・complete table of whole reactions rates including electron capture page 7 ---------------------------------------------------------------------------- Let me summarize this talk. We analyzed the neutrino emissivity of the deuteron bound neutron-neutron reaction and compared that result to the blems. We found that Q_nn for final deuteron state, which has not yet considered in the cooling mechanism, is very large compared with final two-nucleon scattering state, therefore it will be interesting to examine the role of this mechanism in the simulation of supernova evolution. Those are the near future plans. since we have seen rather strong energy dependence of the nuclear matrix element for the deuteron transition, we will re-examine the emissivity for the two-nucleon scattering final state without using ope model or low-energy theorem. Second, We will complete the table of all reactions in two-nucleon system, including election captures.

d shock position t 150ms after core bounce

B: deuteron binding energy : neutron mass fraction : mass density in units of