14.8 Draft: Nu­cleon sep­a­ra­tion en­er­gies

Nu­cleon sep­a­ra­tion en­er­gies are the equiv­a­lent of atomic ion­iza­tion en­er­gies, but for nu­clei. The pro­ton sep­a­ra­tion en­ergy is the min­i­mum en­ergy re­quired to re­move a pro­ton from a nu­cleus. It is how much the rest mass en­ergy of the nu­cleus is less than that of the nu­cleus with one less pro­ton and a free pro­ton.

Fig­ure 14.5: Pro­ton sep­a­ra­tion en­ergy. [pdf][con]
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Fig­ure 14.6: Neu­tron sep­a­ra­tion en­ergy. [pdf][con]
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Sim­i­larly, the neu­tron sep­a­ra­tion en­ergy is the en­ergy needed to re­move a neu­tron. Fig­ures 14.5 and 14.6 show pro­ton and neu­tron sep­a­ra­tion en­er­gies as grey tones. Note that these en­er­gies are quite dif­fer­ent from the av­er­age bind­ing en­ergy per nu­cleon given in the pre­vi­ous sub­sec­tion. In par­tic­u­lar, it takes a lot of en­ergy to take an­other pro­ton out of an al­ready pro­ton-de­fi­cient nu­cleus. And the same for tak­ing a neu­tron out of an al­ready neu­tron de­fi­cient nu­cleus.

In ad­di­tion, the ver­ti­cal strip­ing in 14.5 shows that the pro­ton sep­a­ra­tion en­ergy is no­tice­ably higher if the ini­tial num­ber of pro­tons is even than if it is odd. Nu­cle­ons of the same kind like to pair up. If a pro­ton is re­moved from a nu­cleus with an even num­ber of pro­tons, a pair must be bro­ken up, and that re­quires ad­di­tional en­ergy. The neu­tron sep­a­ra­tion en­ergy 14.6 shows di­ag­o­nal strip­ing for sim­i­lar rea­sons; neu­trons too pair up.

There is also a vis­i­ble step down in over­all grey level at the higher magic num­bers. It is not dra­matic, but real. It il­lus­trates that the nu­cleon en­ergy lev­els come in shells ter­mi­nated by magic num­bers. In fact, this step down in en­ergy de­fines the magic num­bers. That is dis­cussed fur­ther in sec­tion 14.12.

Fig­ure 14.7: Pro­ton pair sep­a­ra­tion en­ergy. [pdf][con]
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Fig­ure 14.8: Neu­tron pair sep­a­ra­tion en­ergy. [pdf][con]
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Fig­ures 14.7 and 14.8 show the en­ergy to re­move two pro­tons, re­spec­tively two neu­trons from even-even nu­clei. This show up the higher magic num­bers more clearly as the pair­ing en­ergy ef­fect is re­moved as a fac­tor.