The magic number in nuclear physics is defined as a number of nucleons consisting of either neutrons or protons separately arranged in a manner of complete shells within their atomic nucleus. Atomic nuclei consisting of a magic number of neutrons and protons are considered much more stable than any other nuclei. As of 2019, the 7 widely recognized magic numbers are 2,8,20,28,50,82,126, with a sequential arrangement of A018226 in their OEIS.
The protons usually correspond with the following elements called oxygen, helium, nickel, calcium, tin, and lead, along with the hypothetical unbihexium, but 126 is so far to be considered as a magic number in terms of neutrons. The atomic nuclei consisting of a magical number in the nucleons are generally occupied with average binding energy, which is very high per nucleon than the one expected based upon the predictions like the semi-empirical mass formula and thus is considered to have much more stability against its nuclear decay. The isotopes with magic numbers have exceptional stability, which means that the transuranium elements can be theoretically created with extremely larger-sized nuclei and still will not be subjected to any extremely rapid radioactive decays, which are typically associated with high atomic numbers. Thus it is assumed that the significant isotopes consisting of magic numbers exist in an island of stability.
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Why are these Numbers Known as the Magic Numbers?
The answer to the question of what is the magic number begins from the Inside of an atomic nucleus, where its neutrons and protons are arranged in the form of shell structures which is similar to the electron shell surrounding an atom. When the neutron and proton shells get filled with 2, 8,20,28,50, and 82, 126 nucleons, they are known as the magic with nuclei in a spherical shape. But when the number of nucleons does not form a magic number, the nuclei lose their spherical shape and get deformed.
As per the recent experimental data, neutron-rich radioactive isotopes can be a significant challenge during the estimation of the magic number as it is the same for all the given nuclei. The neutron-rich isotope 32 of the Mg element is composed of about 20 neutrons and 12 protons and has become deformed due to the absence of magic number 20 of the neutron. A region called the island of deformation in a nuclear chart is made up of elements known to lose their magic number 20 of the neutron. Previously this region was thought to have only a very few nuclei around the isotope 32 of Mg.
Special Features of the Nuclei Having a Magic Number in its Nucleons
It has a nature of higher abundance. Such helium-4 is considered the most stable and abundant nuclei in the whole universe.
All the stable elements at the end of the decay series have a magic number of protons and neutrons. For example, the nuclei of O-16, He-4, and the Pb-208, having 126 neutrons and 82 protons, contain a magic number of protons and neutrons, equally stable.
The nuclei have N= magic number with much lower cross-sections of the neutron absorption than its surrounding isotopes.
The nuclei containing the magic numbers appear to be spherical with absolutely zero electric quadrupled moments.
The nuclei containing the magic number always have a higher first excitation level of energy.
Significance of the Magic Number in Nuclear Physics
The significances of the magic numbers in nuclear physics are as follows:
The magic numbers indicate the number of filled nuclear shells.
They tend to identify the isotopes that are much more stable as compared to other elements.
The magic number shows the energies of each nucleon.
The element that has an atomic number 20 is calcium, and it is doubly magic.
The magic numbers in nuclear physics are described as a number corresponding to its complete shells within its atomic nuclei and is thus considered to be a magic number and the atomic nuclei having such a magic number in its nucleons usually consists of a very high average binding energy per nucleon these magic numbers are usually predicted by its nuclear shell model and are often proved by its observations showing a sudden discontinuity in the energy separations of both protons and neutrons at particular values of N and Z. The magic number in the periodic table with the periodic law forms the most fundamental law of physics responsible for these magic numbers. The magic number example is 2, 8, 20, 28, 50, 82, and 126.
The concept of magic numbers in nuclear physics delves into the intrinsic arrangement of nucleons within atomic nuclei, granting stability and distinct properties to certain configurations. These numbers, such as 2, 8, 20, 28, 50, 82, and 126, denote the count of either neutrons or protons forming complete shells within the nucleus. Their significance arises from the remarkable stability observed in nuclei that possess these specific quantities of nucleons.
Experimental data and observations highlight the enhanced stability and higher binding energy per nucleon in nuclei with magic numbers, contrasting with predictions from models like the semi-empirical mass formula. This increased stability translates into reduced susceptibility to rapid nuclear decay, contributing to the notion of an "island of stability" for these isotopes.
Magic numbers manifest spherical shapes in nuclei, offering insights into their structural integrity. Nuclei conforming to these numbers exhibit distinctive traits like lower neutron absorption cross-sections, zero electric quadrupole moments, and elevated first excitation energies, setting them apart from surrounding isotopes.
The importance of these magic numbers in nuclear physics extends to their role in identifying filled nuclear shells, pinpointing more stable isotopes, and elucidating the energy levels of individual nucleons. Notably, certain elements like calcium (with an atomic number of 20) are doubly magic, possessing both a magic number of protons and neutrons, intensifying their stability.
The periodicity of these magic numbers aligns with the periodic law, forming a fundamental aspect of nuclear physics. These values—2, 8, 20, 28, 50, 82, and 126—underscore the existence of unique nuclear configurations, establishing a crucial framework within the realm of atomic and nuclear structure.
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