dorsal/arxiv
View SchemaThe one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion
| Authors | A. Shebeko, P. Papakonstantinou, E. Mavrommatis |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0602056 |
| URL | https://arxiv.org/abs/nucl-th/0602056 |
| DOI | 10.1140/epja/i2005-10247-3 |
| Journal | Eur.Phys.J. A27 (2006) 143-155 |
Abstract
The one-body and two-body density matrices in coordinate space and their Fourier transforms in momentum space are studied for a nucleus (a nonrelativistic, self-bound finite system). Unlike the usual procedure, suitable for infinite or externally bound systems, they are determined as expectation values of appropriate intrinsic operators, dependent on the relative coordinates and momenta (Jacobi variables) and acting on intrinsic wavefunctions of nuclear states. Thus, translational invariance (TI) is respected. When handling such intrinsic quantities, we use an algebraic technique based upon the Cartesian representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators a^+ and a for oscillator quanta. Each of the relevant multiplicative operators can then be reduced to the form: one exponential of the set {a^+} times other exponential of the set {a}. In the course of such a normal-ordering procedure we offer a fresh look at the appearance of "Tassie-Barker" factors, and point out other model-independent results. The intrinsic wavefunction of the nucleus in its ground state is constructed from a nontranslationally-invariant (nTI) one via existing projection techniques. As an illustration, the one-body and two-body momentum distributions (MDs) for the 4He nucleus are calculated with the Slater determinant of the harmonic-oscillator model as the trial, nTI wavefunction. We find that the TI introduces important effects in the MDs.
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"abstract": "The one-body and two-body density matrices in coordinate space and their\nFourier transforms in momentum space are studied for a nucleus (a\nnonrelativistic, self-bound finite system). Unlike the usual procedure,\nsuitable for infinite or externally bound systems, they are determined as\nexpectation values of appropriate intrinsic operators, dependent on the\nrelative coordinates and momenta (Jacobi variables) and acting on intrinsic\nwavefunctions of nuclear states. Thus, translational invariance (TI) is\nrespected. When handling such intrinsic quantities, we use an algebraic\ntechnique based upon the Cartesian representation, in which the coordinate and\nmomentum operators are linear combinations of the creation and annihilation\noperators a^+ and a for oscillator quanta. Each of the relevant multiplicative\noperators can then be reduced to the form: one exponential of the set {a^+}\ntimes other exponential of the set {a}. In the course of such a normal-ordering\nprocedure we offer a fresh look at the appearance of \"Tassie-Barker\" factors,\nand point out other model-independent results. The intrinsic wavefunction of\nthe nucleus in its ground state is constructed from a\nnontranslationally-invariant (nTI) one via existing projection techniques. As\nan illustration, the one-body and two-body momentum distributions (MDs) for the\n4He nucleus are calculated with the Slater determinant of the\nharmonic-oscillator model as the trial, nTI wavefunction. We find that the TI\nintroduces important effects in the MDs.",
"arxiv_id": "nucl-th/0602056",
"authors": [
"A. Shebeko",
"P. Papakonstantinou",
"E. Mavrommatis"
],
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"nucl-th"
],
"doi": "10.1140/epja/i2005-10247-3",
"journal_ref": "Eur.Phys.J. A27 (2006) 143-155",
"title": "The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion",
"url": "https://arxiv.org/abs/nucl-th/0602056"
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