¾ Spin of many nucleons add to give I. Some basic rules: 1. When they pair their spins either: cancel (spins pair antiparallel) pairing of a spin-up and spin-down nucleon add (spins pair parallel) pairing of two nucleons with both spin up or both spin down which may affect the nuclear force. As nucleons are added in a nucleus in a specific state the nucleons get paired and the final spin state of the nucleus is decided by the odd nucleon (its spin). My understanding is that nucleons have a strong tendency to pair - proton with proton, neutron with neutron, proton with neutron. An example of transitions between a nucleus’s energy levels is shown in Fig. An alpha particle is composed of four nucleons occupying all four combinations, namely it has two protons (having opposite spin) and two neutrons (also having opposite spin) and its net nuclear spin is zero. Since the nucleons get paired-off, the total spin and The ground states of 12B (5 protons, 7 neutrons) and 12N (7 protons, 5 neutrons) are For even number of protons plus even number of neutrons: I0= . This is a consequence of the spin pairings of nucleons, leading to a limited total nuclear angular momentum. Nucleons Hamiltonian 5.3.3 . This will be shown explicitly the example presented in Sec. Most nuclei and their isotopes are unstable. Although the spin-triplet interaction is stronger, the spin-orbit field tends to suppress pairing in the triplet channel [1,2]. This fact is the most strik ing evidence that the residual interaction plays an important role and leads to pairing of nucleons of the same type within an atomic nucleus. Both states have the same energy in the SU(4) limit. 5.1 Characteristics of the nuclear force . 12C, 16O 2. ¾ Pairing dictated by a shell model of nucleus. The isospin and spin quantum numbers of the nucleon have two states each, resulting in four combinations in total. The microscopic calculation of the spin distribution of level densities in the presence of correlations is a difficult problem. Pairing of electrons near the Fermi surface with antiparallel momentum and spin (k up; -k down) • Nuclear physics: Pairing of nucleons to total I Z=0 : (m i , -m ) Experimental observations: Odd-even effect in nuclear physics The nuclear mass for given odd A:-> Binding energy for odd nuclei: Energy gap in nuclear physics for low excitations: In this part of the course we want to study the structure of nuclei. (analogous -not identical- to electron spin pairing) ¾ Protons and neutrons add separately. Stable nuclei are found in a narrow band, in the N-Z diagram which is called the valley of stability. Paired spins → I = 0. This pairing of nucleons implies the existence of a pairing force that lowers the energy of the system when the nucleons are paired-off. Spin pairing and valence nucleons . pairing the down-spin nucleons with each other. valence nucleons outside filled shells, the Shell Model calculations agree very well with measured values of spin and parity assignments and transition probabilities. between identical nucleons in the spin-singlet channel. IV. 6-3. However, spin-triplet pairing becomes fa-vored in nuclei with equal numbers of neutrons N and protons Z when the nucleon number is very large (proba- the spin-spin or spin-orbit interactions will be different for two states. levels are filled the nucleons of each type pair off, yielding a zero angular momentum for the pair. Nuclear angular momentum includes not only nucleon spin but also nucleon orbital angular momentum. 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