1. 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.

2. 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)

3. 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

4. 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

5. 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.

6. 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

7. 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.

8. 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.

9. d
shock position t
150ms after core bounce

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