The isotopes of Calcium

Natural Ca is a mixture of five stable isotopes (⁴⁰Ca, ⁴²Ca, ⁴³Ca, ⁴⁴Ca, and ⁴⁶Ca) and one radioisotope with a half-life so long that it can be thought of as stable for all practical purposes (48Ca, with a half-life of about 4.3 ×10¹⁹ years).

Ca is the first (lightest) element with six naturally occurring isotopes. The most common isotope is ⁴⁰Ca, making up 96.941%. It is formed in the silicon-burning process by fusion of alpha particles and is the heaviest stable nuclide with equal proton and neutron numbers; in addition, its occurrence is supplemented slowly by the decay of primordial 40K. Adding another alpha particle would form unstable ⁴⁴Ti, which rapidly decays via two successive electron captures to stable ⁴⁴Ca, making up 2.806% of all natural calcium and is the second most common isotope. The remaining four naturally occurring isotopes, ⁴²Ca, ⁴³Ca, ⁴⁶Ca, and ⁴⁸Ca, comprise less than 1% each. The four lighter isotopes are mostly formed by the oxygen-burning and silicon-burning processes, while the two heavier ones are formed by neutron-capturing processes.

⁴⁶Ca is mainly formed in a “hot” s-process, as it needs a rather high neutron flux so that short-lived ⁴⁵Ca can capture a neutron. ⁴⁸Ca is formed through electron capture in the r-process in type Ia supernovae, where high neutron excess and low enough entropy guarantee its survival. ⁴⁶Ca and ⁴⁸Ca are the first “classically stable” nuclides with a six-neutron or eight-neutron excess, respectively. While extremely neutron-rich for such a light element, ⁴⁸Ca is very stable as it is a doubly magic nucleus with 20 protons and 28 neutrons arranged in closed shells. Its β decay to ⁴⁸Sc is strongly hindered due to the significant mismatch in nuclear spin: ⁴⁸Ca has zero nuclear spin, being even, whereas ⁴⁸Sc has spin 6 1 , so the decay is forbidden by the conservation of angular momentum. Although two excited states of ⁴⁸Sc are also available for decay, they are also forbidden due to their high spins. Consequently, when ⁴⁸Ca does decay, it does so via double β decay to ⁴⁸Ti instead, making it the lightest nuclide known to undergo double β decay. Theoretically, ⁴⁶Ca can also undergo double β decay to ⁴⁶Ti, but this has never been detected. The lightest and most common isotope, ⁴⁰Ca, is also doubly magic and could undergo double electron capture to ⁴⁰Ar, but similarly, this has never been detected.

Ca is the only element that has two primordial doubly magic isotopes. The experimental lower limits for the half-lives of ⁴⁰Ca and ⁴⁶Ca are 5.9×10²¹ and 2.8 ×10¹⁵ years, respectively. Apart from the practically stable ⁴⁸Ca, the longest-lived radioisotope is ⁴¹Ca, which decays through electron capture to stable 41K with a half-life of 1.03×10⁵ years. Its presence in the early solar system as an extinct radionuclide has been deduced from an excess of 41K: trace amounts of ⁴¹Ca also still exist since it is a cosmogenic nuclide, continuously reformed through neutron activation of natural ⁴⁰Ca.

A large number of other radioisotopes are known, ranging from ³⁴Ca to ⁵⁷Ca: they are all much shorter-lived than ⁴¹Ca, and the most stable among them are ⁴⁵Ca with a half-life of 163 days and ⁴⁷Ca with a half-life of 4.54 days. The isotopes lighter than ⁴²Ca typically undergo β1 decay to isotopes of K. In contrast, those heavier than ⁴⁴Ca typically undergo β2 decay to isotopes of Sc, although near the nuclear drip lines, proton emission and neutron emission begin to be significant decay modes as well.

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