MANYBODY @TIFPA

Situazione 2015: Lorenzo Contessi (studente Ph.D.) Lorenzo Andreoli (laureando LM)

Paolo Mori (laureando LM) Maurizio Dapor (D.R. FBK, 50%)

Simone Taioli(P.R. FBK, 80%) Francesco Pederiva

Research lines• Equation of state of dense nuclear matter - Neutron star cores - Effective

interactions (collaborations: ECT*- Los Alamos NL - Argonne NL - Arizona State University, Tempe)

• Pion-less EFT for a nuclear physics from LQCD calculations at high pion mass (collaborations: Hebrew University of Jerusalem - Orsay - Argonne NL)

• Electron capture matrix elements in stellar plasma (collaborations: FBK - Lawrence Livermore NL - Perugia)

• Nuclear response functions

• Condensed matter physics (collaborations: FBK, Arizona State University, Tempe - Cordoba)

• Development of Quantum Monte Carlo methods (collaborations: Lawrence Livermore NL)

Equation of state

3

We can compute the energy of a matter whose constituents are neutrons and hyperons (sort of “heavy” neutrons), in analogy to what is don for instance for a liquid metal or electron gas with impurities.

General relativity equations allow us to connect the equation of state of matter to the structure of compact stars (the Tolman-Oppenheimer-Volkov equations). These predictions must be compared with astrophysical observations on masses and radii.

M [M

sun]

R [km]

PNM RNM : VRN RNM : VRN+VRNN1

RNM : VRN+VRNN2

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

10 11 12 13 14 15 16

causality2.47 Msun

0.69 Msun

1.33 Msun

outer core: (� 9 km)n p e µ

outer crust:

(0.3÷ 0.5 km)

e Z

inner crust: (1÷ 2 km)e Z n

inner core:

(0÷ 3 km)

n,p,e,𝜇 and maybe hyperons…

R ⇠ 10 kmM ⇠ 1.4M�

E [M

eV]

lb [fm-3]

PNM

RN

RN + RNN (I)

0

20

40

60

80

100

120

140

0.0 0.1 0.2 0.3 0.4 0.5 0.6

parti

cle

fract

ion

lb [fm-3]

n

R R

0.2 0.3 0.4 0.5 0.6

10-2

10-1

100

Can we really constrain 𝛬NN interaction from hyper nuclear data?

In hypernuclei it is possible that the 𝛬NN interaction is not well constrained, especially in the isospin triplet channel:

np

nn

𝝠 𝝠

We are doing the exercise of re-projecting the interaction in the isospin singlet and triplet channels and try to explore the dependence of the hypernuclei binding energy on the relative strength.

⇤NN potential resolved in the NN isospin singlet and triplet

F. Pederiva

The ~⌧i · ~⌧j part of the three-body potential can be written as:

v2⇡,P = �CP6 {Xi�, X�j}~⌧i · ~⌧j

v2⇡,S = CSO2⇡,Sij� ~⌧i · ~⌧j

We want to rewrite these contributions in such a way that they are splitted intoan isospin triplet and an isospin singlet channels, adding then a parameter tocontrol the first with respect to the second.

As always, let us notice that:

~⌧i · ~⌧j = 1� 4PT=0ij = 4PT=1

ij � 3.

We can sum the two expressions multiplying the first by 3, and obtain thefollowing identity:

~⌧i · ~⌧j = �3PT=0ij + PT=1

ij

Now, defining:

vPij� ⌘ vPij�(CS , CP ) = �CP

6{Xi�, X�j}+ CSO

2⇡,Sij�

the isospin-dependent three body potential then becomes:

v⌧⌧ij� = �3vPij�PT=0ij + vPij�P

T=1ij .

We define a new potential by inserting a parameter A that controls the strengthof the potential projected on the isospin triplet channel:

v⌧⌧ij� = �3vPij�PT=0ij +AvPij�P

T=1ij .

A = 0 is the case in which the isospin triplet channel is suppressed. A = 1 is thepresent potential case. However, I think that in this context A could assumearbitrarily large values, and even change sign. Actually, it can be inferred thatif PT=0

ij is the most contributing channel in hypernuclei as expected, the expec-

tation of vPij� should be mostly negative in order to give the observed reductionof B(⇤). This means that under this hypothesis some repulsion might be gainedin neutron matter withouta↵ecting the results in hypernuclei by playing withnegative values of A.

This potential can be easily recast in the usual form useful for AFDMCcalculations in this way:

v⌧⌧ij� =3

4(A� 1)vPij� +

1

4(3 +A)vPij�~⌧i · ~⌧j .

Notice that there is a contribution that has to be added to the isospin indepen-dent part of the interaction as well.

Please check coe�cients, signs etc.

1

v⌧⌧ij� = �3vPij�PT=0ij + CT v

Pij�P

T=1ij

CT=1 gives the original potential, but we can choose an arbitrary value. CT < 1 ⇒ more repulsion

NN isospin singlet NN isospin triplet

Pauli repulsion

must be negative on averageto give repulsion

v⌧⌧ij� =3

4(CT � 1)vPij� +

1

4(3 + CT )v

Pij�~⌧i · ~⌧j

Can we really constrain the interaction from hyper nuclear data?

E / E

(cT=

1)

cT

4RH 4RHe5RHe

17RO

41RCa

49RCa

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

-2.0 -1.0 0.0 1.0 2.0 3.0

Francesco Catalano, Diego Lonardoni, FP, unpublished

small asymmetry

larger asymmetryPRELI

MINAR

Y

QMC in momentum space (CIMC)

6

The idea is to project the ground state of the Hamiltonian restricted to the model Hilbert space chosen by means of a stochastic implementation of the power method.To this end we define the usual projection operator:

P = 1��⌧(H � ET )

ET is a trial eigenvalue used to preserve the normalization of the projected state.

Problems • As the number of state i the model space and/or the particle number

increases the algorithm becomes very inefficient (very small time steps are required)

• For a generic Hamiltonian the matrix elements among two states in the model space can be negative, and the algorithm breaks down.

Possible solution: • IMPORTANCE SAMPLING! In particular we can use wave functions from

Coupled Clusters calculations

QMC in momentum space

Previously published calculations did notinclude 3p-3h correlations in the CC wavefunction. We are now on the way of using inan efficient way CCDT(1) (i.e. triplets at PT level). Extension to finite systems(thereby projecting from CCSD or CCSDT(1)wave functions is in progress (Masterthesis of Paolo Mori)

..........

.....

.....................................................................

.....

......

.....

.....

.

Configuration interaction Monte CarloUse of Coupled Cluster wavefunctions

Electron Gas resultsConclusions

Conclusions

Momentum Distribution (66 neutrons, N2LO)

0.97

0.98

0.99

1

n(k)

0 0.5 1 1.5 2 2.5k/k

F

0

0.01

0.02

Francesco Pederiva MES14, Amasya, Turkey Sep 1-5, 2014

One of the most interesting features ofthis algorithm is the possibility of computingvery accurate momentum distributions, which might be a useful input for othercalculations.

Effective π-less theories

Lorenzo Contessi, FP, Nir Barnea, U. van Kolck

Plan: build a π-less effective Hamiltonian in coordinate space on few-body system and check the results for nuclei with larger masses. Test: a nuclear physics with mπ=800MeV - LQCD calculations available for A=3,4

Λ D ΔD

He3 6 -1069,2 315,2

He3 4 -370,2 116,3

He3 2 -72,3 32,1

VLO = CLO1 + CLO

2 �1 · �2 V 3bLO = D1⌧1 · ⌧2

VLO(r) = (CLO1 + CLO

2 �1 · �2)I0(⇤, r)

Regularization in r space

Ik(⇤, r) = ⇤ke�⇤2r2/4 Calculations with AFDMC ok

Novità (?)

Due nuovi innesti di personale a staff su MANYBODY: Simone Taioli (80%) e Maurizio Dapor (50%). Questo dovrebbe salvare il nodo di TN per i prossimi anni… Possibilità di ottenere finanziamenti di borse Ph.D. da parte di LANL e LLNL (difficoltà nel trasferimento di fondi) Partecipazione al MoU con J-Lab per una theoretical unit INFN a supporto dell’attività sperimentale (nel nostro caso per quanto riguarda la fisica ipernucleare) Conclusa la selezione per 1 post-doc congiunto TIFPA/ECT* che dovrebbe supportare la nostra attivita’.

Via pura, cerion de jir inant desche’ che se pel con chel che aon…