In which case nuclear force is stronger ?
In case of nucleons having parallel spin or opposite spin ?
Please explain the reasons.
In case of nucleons having parallel spin or opposite spin ?
Please explain the reasons.
The nuclear force depends on spin of electron There are no easy and simple answers when it comes to questions about the nuclear force. The force between two nucleons is a complicated residual interaction that leaks outside the color confinement walls of the QCD strong interaction. It is best visualized as due to exchanges of quark - antiquark pairs or mesons. There are multiple mesons involved in the nuclear force and the contribution of an individual meson depends strongly on the spin and parity of the meson under considerstion. The lightest meson is the pion, a pseudoscalar particle (spin 0 but odd parity). The force induced by the exchange of a pion is strongly spin dependent, in fact the pion exchange does not even contribute a force component for nuclei with spherical symmetry and spin 0. Since the deuteron lacks spherical symmetry, it does experience a binding force associated with pion exchange, and since the deuteron is a spin 1 particle, we infer that the pion contribution to the nucleon-nucleon force favors spin aligned over spin opposite orientation. The story does not end here.
There are mesons more massive than the pion that also contribute to nuclear binding. We know this to be the case because many of the most tightly bound nuclei are spin 0 and spherical. By symmetry considerations the pion exchange forces average to 0 for these nuclei, so the more massive omega, sigma, and rho mesons must provide the binding forces. The omega meson is an uncharged spin 1 odd parity (vector) meson. It's is similar to a photon, except that it is massive (782 MeV). Like the coulomb interaction, the exchange of an omega meson contributes a central force as well as a spin-orbit force that is small in comparison to the central force. The sign of the central force from omega meson exchange is repulsive, however, so it cannot be solely responsible for the binding of these nuclei.
Another likely contribution comes from sigma meson exchange. The sigma meson is uncharged even parity and spin 0 (scalar). It's existence was inferred from its likely role in nuclear binding before it was established by experiments, but now it is listed in the particle data tables. Unlike the omega, the sigma meson is a broad resonance with an ill defined mass range (500-600 MeV). As a Yukawa - like interaction, it also yields a central force term and a small spin-orbit term. Unlike the omega central term, hovever, the sigma central term is attractive. This means that the weak central attraction in spherical nuclei must arrive from a cancellation between omega exchange and sigma exchange with the sigma exchange dominating.
There is an interesting difference between the spin orbit contributions from omega and sigma. Unlike the central components where the two exchanges are of opposite signs, the spin orbit contributions from sigma and omega exchanges are additative. This means that the importance of the spin-orbit force relative to the central force is enhanced in direct proportion to the degree of cancellation of the central force components. As a result of this complex interplay, the spin-orbit contribution in the nuclear force becomes a 10% effect unlike the case in atoms where it is a 1% effect.
The rho meson is another vector (spin 1) particle, but unlike the omega, the rho is a charge triplet (-1, 0, 1). It is said to have isospin 1. Because of its isospin, the rho contributions to both central and spin-orbit forces are proportional to the difference between the neutron and proton distributions in a nucleus, so it is less important than the omega. There are likely to be other even more massive mesons that play a small role in nuclear binding, but the spin dependence of these are likely to be similar to those already discussed.
There are no easy and simple answers when it comes to questions about the nuclear force. The force between two nucleons is a complicated residual interaction that leaks outside the color confinement walls of the QCD strong interaction. It is best visualized as due to exchanges of quark - antiquark pairs or mesons. There are multiple mesons involved in the nuclear force and the contribution of an individual meson depends strongly on the spin and parity of the meson under considerstion. The lightest meson is the pion, a pseudoscalar particle (spin 0 but odd parity). The force induced by the exchange of a pion is strongly spin dependent, in fact the pion exchange does not even contribute a force component for nuclei with spherical symmetry and spin 0. Since the deuteron lacks spherical symmetry, it does experience a binding force associated with pion exchange, and since the deuteron is a spin 1 particle, we infer that the pion contribution to the nucleon-nucleon force favors spin aligned over spin opposite orientation. The story does not end here.
There are mesons more massive than the pion that also contribute to nuclear binding. We know this to be the case because many of the most tightly bound nuclei are spin 0 and spherical. By symmetry considerations the pion exchange forces average to 0 for these nuclei, so the more massive omega, sigma, and rho mesons must provide the binding forces. The omega meson is an uncharged spin 1 odd parity (vector) meson. It's is similar to a photon, except that it is massive (782 MeV). Like the coulomb interaction, the exchange of an omega meson contributes a central force as well as a spin-orbit force that is small in comparison to the central force. The sign of the central force from omega meson exchange is repulsive, however, so it cannot be solely responsible for the binding of these nuclei.
Another likely contribution comes from sigma meson exchange. The sigma meson is uncharged even parity and spin 0 (scalar). It's existence was inferred from its likely role in nuclear binding before it was established by experiments, but now it is listed in the particle data tables. Unlike the omega, the sigma meson is a broad resonance with an ill defined mass range (500-600 MeV). As a Yukawa - like interaction, it also yields a central force term and a small spin-orbit term. Unlike the omega central term, hovever, the sigma central term is attractive. This means that the weak central attraction in spherical nuclei must arrive from a cancellation between omega exchange and sigma exchange with the sigma exchange dominating.
There is an interesting difference between the spin orbit contributions from omega and sigma. Unlike the central components where the two exchanges are of opposite signs, the spin orbit contributions from sigma and omega exchanges are additative. This means that the importance of the spin-orbit force relative to the central force is enhanced in direct proportion to the degree of cancellation of the central force components. As a result of this complex interplay, the spin-orbit contribution in the nuclear force becomes a 10% effect unlike the case in atoms where it is a 1% effect.
The rho meson is another vector (spin 1) particle, but unlike the omega, the rho is a charge triplet (-1, 0, 1). It is said to have isospin 1. Because of its isospin, the rho contributions to both central and spin-orbit forces are proportional to the difference between the neutron and proton distributions in a nucleus, so it is less important than the omega. There are likely to be other even more massive mesons that play a small role in nuclear binding, but the spin dependence of these are likely to be similar to those already discussed.
