Summary
Variational computations of the binding energy per particle for various models of nuclear matter are reported. The main purpose is to compare the results corresponding to a «semi-crystallic» structure characterized by correlated density fluctuations of the four spin-isospin nucleon types, with those corresponding to the standard «Fermi gas» homogeneous and isotropic nuclear-matter structure. It is found that, in some cases, the semicrystallic configuration yields more overall attraction (actually less overall repulsion) than the Fermi-gas case, already at (mean) nuclear densities equal to the central density of ordinary (heavy) nuclei. This effect becomes more pronounced at higher (mean) nuclear densities; it can, in most cases, be attributed, at least in part, to the tensor component of the nuclear interaction, that averages to zero in the Fermi-gas case, and yields instead an attractive contribution in configurations with appropriately correlated density fluctuations of the four spin-isospin nucleon states. All computations are based on realistic one-boson exchange nucleon-nucleon potentials. The correlations associated with the strongly repulsive character of the nucleon-nucleon interaction at short range have not been properly accounted for. The results of this paper have therefore no immediate phenomenological implications; whether the effect displayed here is preserved when the repulsive core of the nucleon-nucleon interaction is properly taken into account (both in the computations with and without density fluctuations) remains an open question.
Riassunto
In questo lavoro si riferiscono i risultati di calcoli di tipo variazionale per diversi modelli di materia nucleare. Lo scopo principale è il confronto dei risultati corrispondenti ad una struttura « semicristallina » caratterizzata da fluttuazioni di densità correlate dei quattro stati di spin e isopin nucleonici, con quelli correspondenti alla struttura standard a « gas di Fermi », omogenea e isotropa. Si trova che, in alcuni casi, la configurazione semicristallina fornisce complessivamente più attrazione (o meglio meno repulsione) del caso a gas di Fermi, già a densità (media) pari alla densità centrale dei nuclei (pesanti). Questo effetto diventa più marcato a densità (medie) più alte; può, nella maggioranza dei casi, essere attribuito, almeno in parte, alla componente tensoriale dell’interazione nucleare, che nel caso del gas di Fermi dà un contributo nullo per effetto della isotropia spaziale, e che fornisce invece un contributo attrattivo in configurazioni con fluttuazioni di densità opportunamente correlate dei quattro stati di spin e isospin nucleonici. Tutti i calcoli sono effettuati con potenziali nucleone-nucleone realistici di tipo OBEP.
Реэюме
Приводятся реэультаты вариационных вычислений знергии свяэи наодну частицу для раэличных моделей ядерного вешества. Основная цель работы -сравнить реэультаты, соответствуюшие «полукристаллическ ой» структуре, харак-териэуемой соответствуюшими флчктуациями плотности четырех типов спин-иэоспиновых нуклонных состояний, с реэультатами, соответствуюшими стандартнойструкту ре «Ферми-гаэа» для однородного и иэотропного ядерного вешества. Получается, что в некоторых случаях полукристаллическая конфугурация даетбольщее суммарное притяжение (фактически, меньщее суммарное отталкивание), чем в случае Ферми-гаэа, уже при (средних) ядерных плотностях, равных центральнойплотнос ти обычных (тяжелых) ядер. Этот зффект становится более выраженнымпри больщих (средних) ядерных плотностях. В больщинстве случаев зто можетбыть приписано, по крайней мере частично, тенэорной компонентой ядерного вэаи-модействия, которая в среднем равна нулю в случае Ферми-гаэа, а в рассматриваемомслу чае дает вклад притяжения в конфигурациях с коррелированными соответст-вуюшим обраэом фликтуациями плотности для четырех спин-иэоспиновых нуклонныхсостояний. Все проведенные вычисления баэируются на реалистических нуклон-нуклонных потенциалах с обменом одним боэоном.
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Literatur
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Supported by a Rome University Fellowship.
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Calogero, F., Ragnisco, O. & Palumbo, F. Density fluctuations in nuclear matter. Nuov Cim A 29, 509–547 (1975). https://doi.org/10.1007/BF02734526
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DOI: https://doi.org/10.1007/BF02734526