dorsal/arxiv
View SchemaScales in nuclear matter: Chiral dynamics with pion nucleon form factors
| Authors | N. Kaiser, M. Mühlbauer, W. Weise |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0610060 |
| URL | https://arxiv.org/abs/nucl-th/0610060 |
| DOI | 10.1140/epja/i2006-10159-8 |
| Journal | Eur.Phys.J.A31:53-60,2007 |
Abstract
A systematic calculation of nuclear matter is performed which includes the long-range correlations between nucleons arising from one- and two-pion exchange. Three-body effects from $2\pi$-exchange with excitations of virtual $\Delta(1232)$-isobars are also taken into account in our diagrammatic calculation of the energy per particle $\bar E(k_f)$. In order to eliminate possible high-momentum components from the interactions we introduce at each pion-baryon vertex a form factor of monopole type. The empirical nuclear matter saturation point, $\rho_0 \simeq 0.16 $fm$^{-3}$, $\bar E_0\simeq -16 $MeV, is well reproduced with a monopole mass of $\Lambda \simeq 4\pi f_\pi \simeq 1.16 $GeV. As in the recent approach based on the universal low-momentum $NN$-potential $V_{\rm low-k}$, the inclusion of three-body effects is crucial in order to achieve saturation of nuclear matter. We demonstrate that the dependence of the pion-exchange contributions to $\bar E(k_f)$ on the ''resolution'' scale $\Lambda$ can be compensated over a wide range of $\Lambda$ by counterterms with two ''running'' contact-couplings. As a further application we study the in-medium chiral condensate $<\bar q q >(\rho)$ beyond the linear density approximation. For $\rho \leq 1.5 \rho_0$ we find small corrections from the derivative $d \bar E(k_f)/d m_\pi$, which are stable against variations of the monopole regulator mass $\Lambda$.
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"abstract": "A systematic calculation of nuclear matter is performed which includes the\nlong-range correlations between nucleons arising from one- and two-pion\nexchange. Three-body effects from $2\\pi$-exchange with excitations of virtual\n$\\Delta(1232)$-isobars are also taken into account in our diagrammatic\ncalculation of the energy per particle $\\bar E(k_f)$. In order to eliminate\npossible high-momentum components from the interactions we introduce at each\npion-baryon vertex a form factor of monopole type. The empirical nuclear matter\nsaturation point, $\\rho_0 \\simeq 0.16 $fm$^{-3}$, $\\bar E_0\\simeq -16 $MeV, is\nwell reproduced with a monopole mass of $\\Lambda \\simeq 4\\pi f_\\pi \\simeq 1.16\n$GeV. As in the recent approach based on the universal low-momentum\n$NN$-potential $V_{\\rm low-k}$, the inclusion of three-body effects is crucial\nin order to achieve saturation of nuclear matter. We demonstrate that the\ndependence of the pion-exchange contributions to $\\bar E(k_f)$ on the\n\u0027\u0027resolution\u0027\u0027 scale $\\Lambda$ can be compensated over a wide range of\n$\\Lambda$ by counterterms with two \u0027\u0027running\u0027\u0027 contact-couplings. As a further\napplication we study the in-medium chiral condensate $\u003c\\bar q q \u003e(\\rho)$ beyond\nthe linear density approximation. For $\\rho \\leq 1.5 \\rho_0$ we find small\ncorrections from the derivative $d \\bar E(k_f)/d m_\\pi$, which are stable\nagainst variations of the monopole regulator mass $\\Lambda$.",
"arxiv_id": "nucl-th/0610060",
"authors": [
"N. Kaiser",
"M. M\u00fchlbauer",
"W. Weise"
],
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"nucl-th"
],
"doi": "10.1140/epja/i2006-10159-8",
"journal_ref": "Eur.Phys.J.A31:53-60,2007",
"title": "Scales in nuclear matter: Chiral dynamics with pion nucleon form factors",
"url": "https://arxiv.org/abs/nucl-th/0610060"
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