On nuclear short-range correlations and the zero-energy eigenstates of the Schrodinger equation

Nir Barnea; Ronen Weiss; Saar Beck

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On nuclear short-range correlations and the zero-energy eigenstates of the Schrodinger equation

Saar Beck, Ronen Weiss, Nir Barnea

Nuclear Theory · Submitted 27 Dec 2022

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The authors' main claim To this end we analyze the doublet and triplet Coupled-Cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state.

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arXiv ID2212.13412 (version 1)

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CitationNir Barnea, Ronen Weiss, Saar Beck. "On nuclear short-range correlations and the zero-energy eigenstates of the Schrodinger equation." arXiv:2212.13412 (2022). https://pith.science/paper/3EKNNI2Q

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We present a systematic analysis of the nuclear 2 and 3-body short range correlations, and their relations to the zero-energy eigenstates of the Schrodinger equation. To this end we analyze the doublet and triplet Coupled-Cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state. Furthermore, we find that these Coupled-Cluster amplitudes coincide with the zero-energy Bloch-Horowitz operator. These results illuminate the relations between the nuclear many-body theory and the generalized contact formalism, introduced to describe the nuclear 2-body short range correlations, and it might also be helpful for general Coupled-Cluster computations as the asymptotic part of the amplitudes is given and shown to be universal.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a systematic analysis of the nuclear 2 and 3-body short range correlations, and their relations to the zero-energy eigenstates of the Schrodinger equation.	contribution 1.00	0.93	0.14	asserted 0.89
s1	To this end we analyze the doublet and triplet Coupled-Cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state.	method 0.71	0.93	0.22	asserted 1.00
s2	Furthermore, we find that these Coupled-Cluster amplitudes coincide with the zero-energy Bloch-Horowitz operator.	result 1.00	0.93	0.28	asserted 1.00
s3	These results illuminate the relations between the nuclear many-body theory and the generalized contact formalism, introduced to describe the nuclear 2-body short range correlations, and it might also be helpful for general Coupled-Cluster computations as the asymptotic part of the amplitudes is given and shown to be universal.	interpretation 1.00	0.68	0.23	speculative 0.50

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Original abstract

We present a systematic analysis of the nuclear 2 and 3-body short range correlations, and their relations to the zero-energy eigenstates of the Schrodinger equation. To this end we analyze the doublet and triplet Coupled-Cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state. Furthermore, we find that these Coupled-Cluster amplitudes coincide with the zero-energy Bloch-Horowitz operator. These results illuminate the relations between the nuclear many-body theory and the generalized contact formalism, introduced to describe the nuclear 2-body short range correlations, and it might also be helpful for general Coupled-Cluster computations as the asymptotic part of the amplitudes is given and shown to be universal.

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Also $τ̂_3$ is related to the 3-body CC amplitude asymptotics [ref] and admits the relation $τ^a_1a_2a_3_i_1i_2i_3= (t^∞)^a_1a_2a_3_i_1i_2i_3$.

The asymptotic behaviour of the many-body coupled cluster amplitudes · Assumptions and Main Results · 0.83

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Cites as support 3 papers

The asymptotic factorization, including the definition of the universal two-body functions, is the underlying assumption for the GCF predictions, and was verified numerically using ab-initio calculations [ref] .

Generalized nuclear contacts and the nucleon's momentum distributions · Introduction · 0.96
The asymptotic factorization, including the definition of the universal two-body functions, is the underlying assumption for the GCF predictions, and was verified numerically using ab-initio calculations [ref] .

The nuclear contacts and short range correlations in nuclei · Introduction · 0.96
The asymptotic factorization, including the definition of the universal two-body functions, is the underlying assumption for the GCF predictions, and was verified numerically using ab-initio calculations [ref] .

Scale and Scheme Independence and Position-Momentum Equivalence of Nuclear Short-Range Correlations · Introduction · 0.96

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