Spin states and the equations of motion for a few nucleons

We apply the functional renormalization group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The evolution of the coupling constants in this action is described by a renormalization group flow. We derive these flow equations both in the limit of exact Wigner SU(4) symmetry and in the realistic case of broken symmetry. In the symmetric limit we find that the renormalization flow equations decouple and can be combined into two sets, one of which matches the known results for bosons, and the other result matches the one for a single flavor of spin $1/2$ fermions. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and spin-quintet channels.We apply the functional renormalization group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The evolution of the coupling constants in this action is described by a renormalization group flow. We derive these flow equations both in the limit of exact Wigner SU(4) symmetry and in the realistic case of broken symmetry. In the symmetric limit we find that the renormalization flow equations decouple and can be combined into two sets, one of which matches the known results for bosons, and the other result matches the one for a single flavor of spin $1/2$ fermions. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and spin-quintet channels.

arXiv:1207.5735Physical Review CMay 8, 20137 citations

WAVE FUNCTIONS AND EQUATIONS OF MOTION FOR PARTICLES WITH ARBITRARY SPIN

Yu.V. Novozhilov

Elsevier eBooksJan 1, 19750 citations

A search for the classical model of spin

Mirjana Božić, Z. Marić

Foundations of PhysicsMay 1, 19932 citations

Nucleon momentum distributions, their spin-isospin dependence, and short-range correlations

Massimiliano Alvioli, C. Ciofi degli Atti, L. P. Kaptari +2 more

The nucleon momentum distribution ${n}_{A}(k)$ for $A=2$ , 3, 4, 16, and 40 nuclei is systematically analyzed in terms of wave functions resulting from advanced solutions of the nonrelativistic Schr\"odinger equation, obtained within different many-body approaches based upon different realistic bare nucleon-nucleon ( $NN$ ) interactions featuring similar short-range repulsion and tensor interactions. Particular attention is paid to the separation of the momentum distributions into the mean-field and short-range correlation (SRC) contributions. It is shown that although at high values of the momentum $k$ different approaches lead to some quantitative differences, these do not hinder the general conclusion that the high-momentum behavior ($k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$) of all nuclei considered are very similar, exhibiting the well-known scaling behavior with the mass number $A$ , independently of the used many-body approach and the details of the bare $NN$ interaction. To analyze and understand the frequently addressed question concerning the relationships between the nucleus, ${n}_{A}(k)$ , and the deuteron, ${n}_{D}(k)$ , momentum distributions, the spin ( $S$ )-isospin ( $T$ ) structure of few-nucleon systems and complex nuclei is analyzed in terms of realistic $NN$ interactions and many-body approaches. To this end, the number of $NN$ pairs in a given ( $ST$ ) state, viz., $(ST)=(10)$ , (00), (01), and (11), and the contribution of these states to the nucleon momentum distributions are calculated. It is shown that, apart from the (00) state, which has very small effects, all other spin-isospin states contribute to the momentum distribution in a wide range of momenta. It is shown that for all nuclei considered the momentum distributions in the states $T=0$ and $T=1$ exhibit at $k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$ very similar behaviors, which represents strong evidence of the $A$ -independent character of SRCs. The ratio ${n}_{A}(k)/{n}_{D}(k)$ is analyzed in detail, stressing that in the SRC region it always increases with the momentum and the origin of such an increase is discussed and elucidated. The relationships between the one- and two-body momentum distributions, considered in a previous paper, are discussed and clarified, pointing out the relevant role played by the center-of-mass motion of a correlated pair in the (10) state. Eventually, the values of the the probability of high-momentum components in nuclei and the per nucleon probability ${a}_{2}$ of deuteronlike configurations in nuclei are calculated, and the relationship of the present approach with the many-body methods based upon low-momentum effective interactions is briefly discussed.The nucleon momentum distribution ${n}_{A}(k)$ for $A=2$, 3, 4, 16, and 40 nuclei is systematically analyzed in terms of wave functions resulting from advanced solutions of the nonrelativistic Schr\"odinger equation, obtained within different many-body approaches based upon different realistic bare nucleon-nucleon ($NN$) interactions featuring similar short-range repulsion and tensor interactions. Particular attention is paid to the separation of the momentum distributions into the mean-field and short-range correlation (SRC) contributions. It is shown that although at high values of the momentum $k$ different approaches lead to some quantitative differences, these do not hinder the general conclusion that the high-momentum behavior ($k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$) of all nuclei considered are very similar, exhibiting the well-known scaling behavior with the mass number $A$, independently of the used many-body approach and the details of the bare $NN$ interaction. To analyze and understand the frequently addressed question concerning the relationships between the nucleus, ${n}_{A}(k)$, and the deuteron, ${n}_{D}(k)$, momentum distributions, the spin ($S$)-isospin ($T$) structure of few-nucleon systems and complex nuclei is analyzed in terms of realistic $NN$ interactions and many-body approaches. To this end, the number of $NN$ pairs in a given ($ST$) state, viz., $(ST)=(10)$, (00), (01), and (11), and the contribution of these states to the nucleon momentum distributions are calculated. It is shown that, apart from the (00) state, which has very small effects, all other spin-isospin states contribute to the momentum distribution in a wide range of momenta. It is shown that for all nuclei considered the momentum distributions in the states $T=0$ and $T=1$ exhibit at $k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$ very similar behaviors, which represents strong evidence of the $A$-independent character of SRCs. The ratio ${n}_{A}(k)/{n}_{D}(k)$ is analyzed in detail, stressing that in the SRC region it always increases with the momentum and the origin of such an increase is discussed and elucidated. The relationships between the one- and two-body momentum distributions, considered in a previous paper, are discussed and clarified, pointing out the relevant role played by the center-of-mass motion of a correlated pair in the (10) state. Eventually, the values of the the probability of high-momentum components in nuclei and the per nucleon probability ${a}_{2}$ of deuteronlike configurations in nuclei are calculated, and the relationship of the present approach with the many-body methods based upon low-momentum effective interactions is briefly discussed.

arXiv:1211.0134Physical Review CMar 5, 201354 citations

A new approach to the theory of the spin

Austin Blaquière

International Journal of Non-Linear MechanicsJan 1, 19801 citation

1/2

fermions. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and spin-quintet channels.

The nucleon momentum distribution

{n}_{A}(k)

for

A=2

, 3, 4, 16, and 40 nuclei is systematically analyzed in terms of wave functions resulting from advanced solutions of the nonrelativistic Schr\"odinger equation, obtained within different many-body approaches based upon different realistic bare nucleon-nucleon (

NN

) interactions featuring similar short-range repulsion and tensor interactions. Particular attention is paid to the separation of the momentum distributions into the mean-field and short-range correlation (SRC) contributions. It is shown that although at high values of the momentum

k

different approaches lead to some quantitative differences, these do not hinder the general conclusion that the high-momentum behavior ($k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$) of all nuclei considered are very similar, exhibiting the well-known scaling behavior with the mass number

A

, independently of the used many-body approach and the details of the bare

NN

interaction. To analyze and understand the frequently addressed question concerning the relationships between the nucleus,

{n}_{A}(k)

, and the deuteron,

{n}_{D}(k)

, momentum distributions, the spin (

S

)-isospin (

T

) structure of few-nucleon systems and complex nuclei is analyzed in terms of realistic

NN

interactions and many-body approaches. To this end, the number of

NN

pairs in a given (

ST

) state, viz.,

(ST)=(10)

, (00), (01), and (11), and the contribution of these states to the nucleon momentum distributions are calculated. It is shown that, apart from the (00) state, which has very small effects, all other spin-isospin states contribute to the momentum distribution in a wide range of momenta. It is shown that for all nuclei considered the momentum distributions in the states

T=0

and

T=1

exhibit at $k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$ very similar behaviors, which represents strong evidence of the

A

-independent character of SRCs. The ratio

{n}_{A}(k)/{n}_{D}(k)

is analyzed in detail, stressing that in the SRC region it always increases with the momentum and the origin of such an increase is discussed and elucidated. The relationships between the one- and two-body momentum distributions, considered in a previous paper, are discussed and clarified, pointing out the relevant role played by the center-of-mass motion of a correlated pair in the (10) state. Eventually, the values of the the probability of high-momentum components in nuclei and the per nucleon probability

{a}_{2}

of deuteronlike configurations in nuclei are calculated, and the relationship of the present approach with the many-body methods based upon low-momentum effective interactions is briefly discussed.