arXiv subjects

S. Szpigel

Publications and source records attributed to S. Szpigel.

16 recordsLinked to original sources

arXiv2021

On-shell transition of SRG and nuclear systems

We make variational estimates for the binding energies of $^2H,~^3H,~^4He,~^{16}O,~^{40}Ca$, showing their running with the Similarity Renormalization Group (SRG) cutoff towards the infrared region and show the generalized Tjon lines that emerge from the calculations. We infer the SRG evolution of the three-body contributions for the $^3H$ and $^4He$ binding energies by computing the two-body contributions with a variational approach assuming that four-body forces are negligible. At any given SRG cutoff, the three-body contributions may then be inferred as being the experimental value minus the two-body contributions. The off-shell / on-shell transition at a critical SRG cutoff $λ_c$ drives the behavior of all binding energies and this scale is the turning point of the generalized Tjon lines. Also, at $λ_c$ the ratios between three-body and two-body contributions to the binding energies, $B_{λ_c}(3) ~/~ B_{λ_c}(2)$, are the same in both $^3H$ and $^4He$ systems and equal to $1/4$, so that $B_{λ_c}(2) ~=~ 4~B_{λ_c}(3)$. All calculations are carried out with the Idaho-Salamanca N3LO potential, which is evolved with the SRG up to the infrared fixed point ($λ\to 0$) in all S, P, D, F and G partial-wave channels in order to compute the variational binding energies at several SRG cutoff scales.

nucl-th↗

arXiv2020

FLUKA Simulations of Pion Decay Gamma-radiation from Energetic Flare Ions

Gamma-ray continuum at > 10 MeV photon energy yields information on > 0.2 - 0.3 GeV/nucleon ions at the Sun. We use the general-purpose Monte Carlo code FLUKA (FLUktuierende KAskade) to model the transport of ions injected into thick and thin target sources, the nuclear processes that give rise to pions and other secondaries and the escape of the resulting photons from the atmosphere. We give examples of photon spectra calculated with a range of different assumptions about the primary ion velocity distribution and the source region. We show that FLUKA gives results for pion decay photon emissivity in agreement with previous treatments. Through the directionality of secondary products, as well as Compton scattering and pair production of photons prior to escaping the Sun, the predicted spectrum depends significantly on the viewing angle. Details of the photon spectrum in the 100 MeV range may constrain the angular distribution of primary ions and the depths at which they interact. We display a set of thick-target spectra produced making various assumptions about the incident ion energy and angular distribution and the viewing angle. If ions are very strongly beamed downward, or ion energies do not extend much above 1 GeV/nucleon, the photon spectrum is highly insensitive to details of the ion distribution. Under the simplest assumptions, flares observed near disc centre should not display significant radiation above 1 GeV photon energy. We give an example application to Fermi Large Area Telescope data from the flare of 12 June 2010.

astro-ph.HE↗

arXiv2017

An exact solution to the Bertsch problem and the non-universality of the Unitary Fermi Gas

We analyze the universality of the Unitary Fermi Gas in its ground state from a Wilsonian renormalization point of view and compute the effective range dependence of the Bertsch parameter $ξ$ exactly. To this end we construct an effective block-diagonal two-body separable interaction with the Fermi momentum as a cut-off which reduces the calculation to the mean field level. The interaction is separable in momentum space and is determined by Tabakin's inverse scattering formula. For a vanishing effective range we get $ξ= \frac{176}{9 π}-\frac{17}{3} = 0.56$. By using phase-equivalent similarity transformations we can show that there is a class of exact solutions with any value in the range $ 0.56 \ge ξ\ge -1/3$.

cond-mat.quant-gas↗

arXiv2017

The BCS pairing gap in the on-shell limit of the Similarity Renormalization Group

The pairing gap plays a fundamental role in the nuclear many-body problem and many large scale and accurate mass formula fits suggest the smooth nuclear mass dependence $Δ\sim 6(1)~ A^{-1/3}~{\rm MeV}$ in the liquid drop model which lacks a theoretical motivation. Within the BCS theory we analyze the impact of phase equivalent interactions on the pairing gap for a translational invariant many-fermion system such as nuclear and neutron matter. To that end we use explicitly the Similarity Renormalization Group (SRG) transformations. We show that in the on-shell and continuum limits the pairing gap vanishes. For finite size systems the pairing gap can be computed directly from the scattering phase-shifts by the formula $$ Δ_{nn} (p_F) = Δε_F ~ δ^{^1S_0}_{nn}(p_F) /π~ , $$ where $p_F$ is the Fermi momentum and $Δε_F$ the level spacing at the Fermi energy which for the harmonic oscillator shell model becomes $Δε_F= \hbar ω\sim 41 ~ A^{-1/3}~{\rm MeV}$, so that $$ Δ_{nn} (p_F) \sim 4 ~ A^{-1/3}~{\rm MeV} ~ . $$ The comparison with double differences from binding energies of stable nuclei is satisfactory and the discrepancy with the large scale analysis may be attributed to the lack of three-body forces. Nevertheless, the on-shell two-body interaction provides a basis for the $c~A^{-1/3}$ dependency and accounts for 75\% of the coefficient $c$.

nucl-th↗

arXiv2017

Renormalization of chiral nuclear forces with multiple subtractions in peripheral channels

We analyse the renormalization of the of two-nucleon interaction with multiple subtractions in peripheral waves considering two chiral forces at N3LO. Phase shifts at low energies are then computed with several subtraction points below μ= 10 / fm. We show that for most peripheral waves the phase shifts have nearly no dependence on the renormalization scale. In two cases the phase shifts converge slowly as the renormalization scale approaches μ= 1 / fm and in one case the phase shifts presented oscillations with respect to the subtraction point μ.

nucl-th↗

arXiv2016

Phase transition in the SRG flow of nuclear interactions

We use a chiral interaction at N3LO in the 1S0 channel of the nucleon- nucleon interaction in order to investigate the on-shell transition along the similarity renormalization group flow towards the infrared limit. We find a crossover at a scale that depends on the number of grid points used to discretise the momentum space.

nucl-th↗

arXiv2016

Fixed points of the SRG evolution and the on-shell limit of the nuclear force

We study the infrared limit of the similarity renormalization group (SRG) using a simple toy model for the nuclear force aiming to investigate the fixed points of the SRG evolution with both the Wilson and the Wegner generators. We show how a fully diagonal interaction at the similarity cutoff $λ\rightarrow 0$ may be obtained from the eigenvalues of the hamiltonian and quantify the diagonalness by means of operator norms. While the fixed points for both generators are equivalent when no bound-states are allowed by the interaction, the differences arising from the presence of the Deuteron bound-state can be disentangled very clearly by analyzing the evolved interactions in the infrared limit $λ\to 0$ on a finite momentum grid. Another issue we investigate is the location on the diagonal of the hamiltonian in momentum-space where the SRG evolution places the Deuteron bound-state eigenvalue once it reaches the fixed point. This finite momentum grid setup provides an alternative derivation of the celebrated trace identities, as a by product. The different effects due to either the Wilson or the Wegner generators on the binding energies of $A=2,3,4$ systems are investigated and related to the ocurrence of a Tjon-line which emerges as the minimum of an avoided crossing between $E_α= 4 E_t - 3 E_d$ and $E_α= 2 E_t $. All infrared features of the flow equations are illustrated using the toy model for the two-nucleon $S$-waves.

nucl-th↗

arXiv2014

The infrared limit of the Similarity Renormalization Group evolution and Levinson's theorem

On a finite momentum grid with N integration points and weights the Similarity Renormalization Group (SRG) with a given generator G unitarily evolves an initial interaction with a cutoff on energy differences. This steadily drives the starting Hamiltonian in momentum space to a diagonal form in the infrared limit corresponding to a permutation of the eigenvalues and depends on G. Levinson's theorem establishes a relation between phase-shifts and the number of bound-states. We show that unitarily equivalent Hamiltonians on the grid generate reaction matrices which are compatible with Levinson's theorem but are phase-inequivalent along the SRG trajectory. An isospectral definition of the phase-shift in terms of an energy-shift is possible but requires in addition a proper ordering of states on a momentum grid in order to fulfill Levinson's theorem. We show how the SRG with different generators G induces different isospectral flows in the presence of bound-states, leading to distinct orderings in the infrared limit. While the Wilson generator induces an ascending ordering incompatible with Levinson's theorem, the Wegner generator provides a much better ordering, although not the optimal one. We illustrate the discussion with the nucleon-nucleon (NN) interaction in the 1S0 and 3S1 channels.

nucl-th↗

arXiv2014

Fixed points of the Similarity Renormalization Group and the Nuclear Many-Body Problem

The Similarity Renormalization Group reduces the off-shellness by driving the evolved interaction towards a diagonal band. We analyze the infrared limit and the corresponding on-shell interactions and its consequences for light nuclei. Using a harmonic oscillator shell model we obtain a Tjon line B(4He)= 4B(3H)-3B(2H) which can be understood from a combinatorics counting of nucleon pairs and triplets in the triton and alpha-particle and compares favorably with realistic calculations.

nucl-th↗

arXiv2013

Implicit vs Explicit Renormalization and Effective Interactions

Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the first method is numerically involved, the second one can be solved almost analytically. In both cases we compare the out coming effective interactions for the two nucleon system as functions of the cut-off scale and find a strikingly wide energy region where both approaches overlap, corresponding to relevant scales in light nuclei about 200MeV. This amounts to a great simplification in the determination of the effective interaction parameters.

nucl-th↗

arXiv2013

Nuclear Symmetries of the similarity renormalization group for nuclear forces

We review the role played by long-distance symmetries within the context of the similarity renormalization group approach. This is based on phase-shift-preserving continuous unitary transformations that evolve Hamiltonians with a cutoff on energy differences. We find that there is a similarity cutoff of 3/fm for which almost perfect fulfillment of Wigner SU(4) symmetry is found at the two body level. This suggests to look for similar symmetry patterns for three- and four-body forces. We also analyze the impact of potentials based on Chiral Perturbation Theory in Nuclear Structure calculations.

nucl-th↗

arXiv2011

Renormalization group invariance in pionless effective field theory for the NN system

We consider the NN interaction in pionless effective field theory (EFT) up to next-to-next-to-leading order (NNLO) and use a recursive subtractive renormalization scheme to describe NN scattering in the 1S0 channel. We fix the strengths of the contact interactions at a reference scale, chosen to be the one that provides the best fit for the phase-shifts, and then slide the renormalization scale by evolving the driving terms of the subtracted Lippmann-Schwinger equation through a non-relativistic Callan-Symanzik equation. The results show that such a systematic renormalization scheme with multiple subtractions is fully renormalization group invariant.

nucl-th↗

arXiv2011

Similarity renormalization group evolution of $NN$ interactions within a subtractive renormalization scheme

We apply the similarity renormalization group (SRG) approach to evolve a nucleon-nucleon ($NN$) interaction in leading-order (LO) chiral effective field theory (ChEFT), renormalized within the framework of the subtracted kernel method (SKM). We derive a fixed-point interaction and show the renormalization group (RG) invariance in the SKM approach. We also compare the evolution of $NN$ potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS) equation and the evolution with the similarity cutoff through the SRG transformation.

nucl-th↗

arXiv2009

Charm and longitudinal structure functions with the Kharzeev-Levin-Nardi model

We use the Kharzeev-Levin-Nardi model of the low $x$ gluon distributions to fit recent HERA data on charm and longitudinal structure functions. Having checked that this model gives a good description of the data, we use it to predict $F^c_2$ and $F_L$ to be measured in a future electron-ion collider. The results interpolate between those obtained with the de Florian-Sassot and Eskola-Paukkunen-Salgado nuclear gluon distributions. The conclusion of this exercise is that the KLN model, simple as it is, may still be used as an auxiliary tool to make estimates both for heavy ion and electron-ion collisions.

hep-ph↗

arXiv1998

Mapping of composite hadrons into elementary hadrons and effective hadronic Hamiltonians

A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces and shares similarities with the quasiparticle method of Weinberg. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, hermitian Hamiltonians with a clear physical interpretation are obtained. Applications and comparisons with other composite-particle formalisms of the recent literature are made using the nonrelativistic quark model.

hep-ph↗

arXiv1995

Second quantization approach to composite hadron interactions in quark models

Starting from the Fock space representation of hadron bound states in a quark model, a change of representation is implemented by a unitary transformation such that the composite hadrons are redescribed by elementary-particle field operators. Application of the unitary transformation to the microscopic quark Hamiltonian gives rise to effective hadron-hadron, hadron-quark, and quark-quark Hamiltonians. An effective baryon Hamiltonian is derived using a simple quark model. The baryon Hamiltonian is free of the post-prior discrepancy which usually plagues composite-particle effective interactions.

hep-ph↗