[Paper Review] Nuclear matter properties with the re-evaluated coefficients of liquid drop model

P. Chowdhury, D. N. Basu|ArXiv.org|Aug 4, 2004

Nuclear physics research studies2 references3 citations

TL;DR

This paper re-evaluates the coefficients of the semiempirical liquid drop model using the latest Audi-Wapstra-Thibault atomic mass data via least-squares fitting to minimize chi-square and mean square deviation. It derives improved nuclear matter properties, including a nuclear incompressibility of 290–300 MeV and a mean free path of 3.89–3.91 fm, in excellent agreement with experimental and theoretical estimates.

ABSTRACT

The coefficients of the volume, surface, coulomb, asymmetry and pairing energy terms of the semiempirical liquid drop model mass formula have been determined by furnishing best fit to the observed mass excesses. Slightly different sets of the weighting parameters for liquid drop model mass formula have been obtained from minimizations of chisquare and mean square deviation. The most recent experimental and estimated mass excesses from Audi-Wapstra-Thibault atomic mass table have been used for the least square fitting procedure. Equation of state, nuclear incompressibility, nuclear mean free path and the most stable nuclei for corresponding atomic numbers, all are in good agreement with the experimental results.

Motivation & Objective

• To re-evaluate the coefficients of the semiempirical liquid drop model using the most recent atomic mass data.
• To determine optimal sets of energy coefficients (volume, surface, Coulomb, asymmetry, pairing) by minimizing both chi-square and mean square deviation.
• To investigate the implications of these re-evaluated coefficients on key nuclear matter properties such as incompressibility and mean free path.
• To predict the most stable nuclei across the nuclear chart using the derived coefficients and compare with experimental observations.
• To assess the consistency of the model with experimental constraints on nuclear matter saturation and equation of state.

Proposed method

• Performed a five-parameter least-squares fit to atomic mass excess data from the Audi-Wapstra-Thibault 2003 atomic mass evaluation.
• Used two distinct minimization criteria: chi-square and mean square deviation, yielding slightly different coefficient sets.
• Applied the Bethe-Weizsäcker mass formula with terms for volume, surface, Coulomb, asymmetry, and pairing energy to fit observed mass excesses.
• Derived the nuclear incompressibility from the saturation energy and density using the equation of state derived from the fitted coefficients.
• Calculated the nuclear mean free path using the density-dependent parameter β and nuclear saturation density ρ₀ = 0.1533 fm⁻³.
• Predicted the most stable nuclei by minimizing the binding energy per nucleon using the derived coefficients and compared with experimental nuclide chart data.

Experimental results

Research questions

• RQ1 What are the optimal values of the liquid drop model coefficients when fitted to the latest atomic mass data using chi-square and mean square deviation minimization?
• RQ2 How do the re-evaluated coefficients affect the predicted nuclear incompressibility and how do they compare with experimental estimates?
• RQ3 What is the resulting nuclear mean free path derived from the re-evaluated density-dependent parameter β?
• RQ4 How well do the predicted most stable nuclei (Z vs. N) match the observed stable isotopes from the recent nuclide chart?
• RQ5 To what extent do the fitted coefficients improve the prediction of nuclear binding energy and related properties like separation energies?

Key findings

• The chi-square and mean square deviation minimization procedures yield slightly different sets of coefficients, indicating that both cannot be minimized simultaneously with the same parameter set.
• The nuclear incompressibility derived from the saturation energy and density is 290–300 MeV, in excellent agreement with experimental values from GMR and hard photon emission in heavy-ion collisions.
• The density-dependent parameter β = 1.668 fm² leads to a nuclear mean free path of 3.89–3.91 fm, consistent with other theoretical and experimental estimates.
• The predicted most stable nuclei, derived from the fitted coefficients, show excellent agreement with observed stable isotopes in the nuclide chart.
• The asymmetry energy coefficient and Coulomb coefficient are refined to values that improve consistency with nuclear matter saturation and observed mass trends.
• The model predicts that the most stable nuclei follow a Z vs. N relationship closely matching the theoretical curve derived from the binding energy minimization condition.