14.3 Draft: Overview of Nu­clei

This sec­tion in­tro­duces ba­sic ter­mi­nol­ogy and con­cepts of nu­clei. It also gives an overview of the ways that they can de­cay.

The num­ber of pro­tons in a nu­cleus is called its “atomic num­ber” $Z$. Since each pro­ton has an elec­tric charge $e$, equal to 1.602 18 10$\POW9,{-19}$ C, the to­tal nu­clear charge is $Ze$. While pro­tons at­tract nearby pro­tons and neu­trons in the nu­cleus with the short-range nu­clear force, they also re­pel other pro­tons by the long-range Coulomb force. This force too is very strong at nu­clear dis­tances. It makes nu­clei with more than 82 pro­tons un­sta­ble, be­cause for such large nu­clei the longer range of the Coulomb forces be­comes a ma­jor fac­tor.

The num­ber of neu­trons in a nu­cleus is its neu­tron num­ber $N$. Neu­trons have no charge, so they do not pro­duce Coulomb re­pul­sions. There­fore, the right amount of neu­trons has a sta­bi­liz­ing ef­fect on nu­clei. How­ever, too many neu­trons is not sta­ble ei­ther, be­cause neu­trons by them­selves are un­sta­ble par­ti­cles that fall apart in about 10 min­utes. Com­bined with pro­tons in a nu­cleus, neu­trons can be sta­ble.

Since neu­trons have no charge, they also do not at­tract the elec­trons in the atom or mol­e­cule that the nu­cleus is in. There­fore only the atomic num­ber $Z$ is of much rel­e­vance for the chem­i­cal prop­er­ties of an atom. It de­ter­mines the po­si­tion in the pe­ri­odic ta­ble of chem­istry, chap­ter 5.9. Nu­clei with the same atomic num­ber $Z$, so with the same place in the pe­ri­odic ta­ble, are called “iso­topes.” (In Greek, iso means equal and topos place.)

How­ever, the num­ber of neu­trons does have a sec­ondary ef­fect on the chem­i­cal prop­er­ties, be­cause it changes the mass of the nu­cleus. And the num­ber of neu­trons is of crit­i­cal im­por­tance for the nu­clear prop­er­ties. Nu­clei with the same num­ber of neu­trons are called “iso­tones.” How clever, to re­place the p in iso­topes with an n.

The name of a nu­cleus in­di­cates its num­ber of pro­tons $Z$; for ex­am­ple, hy­dro­gen” means $Z=1$, “he­lium $Z=2$. To also in­di­cate the num­ber of neu­trons, the con­ven­tion is to fol­low the name by the “mass num­ber, or “nu­cleon num­ber” $A$ $\vphantom0\raisebox{1.5pt}{$=$}$ $N+Z$. It gives the to­tal num­ber of nu­cle­ons in the nu­cleus.

For ex­am­ple, the nor­mal hy­dro­gen nu­cleus, which con­sists of a lone pro­ton, is hy­dro­gen-1. The deu­terium nu­cleus, which con­tains both a pro­ton and a neu­tron, is hy­dro­gen-2, in­di­cat­ing that it con­tains two nu­cle­ons to­tal. Be­cause it has the same charge as the nor­mal hy­dro­gen nu­cleus, a deu­terium atom be­haves chem­i­cally al­most the same as a nor­mal hy­dro­gen atom. For ex­am­ple, you can cre­ate wa­ter with deu­terium and oxy­gen just like you can with nor­mal hy­dro­gen and oxy­gen. Such wa­ter is called “heavy wa­ter.” Don’t drink it, how­ever; the dif­fer­ence in chem­i­cal prop­er­ties is still suf­fi­cient to up­set bi­o­log­i­cal sys­tems. Trace amounts are harm­less, as can be ap­pre­ci­ated from the fact that deu­terium oc­curs nat­u­rally. About 1 in 6 500 hy­dro­gen nu­clei in wa­ter on earth are deu­terium ones.

The nor­mal he­lium nu­cleus con­tains two pro­tons plus two neu­trons, so it is called he­lium-4. There is a sta­ble iso­tope, he­lium-3, that has only one neu­tron. In the at­mos­phere, one in a mil­lion he­lium atoms has a he­lium-3 nu­cleus. While nor­mally, there is no big dif­fer­ence be­tween the two iso­topes, at very low cryo­genic tem­per­a­tures they do be­have very dif­fer­ently. The rea­son is that both pro­tons and neu­trons have spin $\leavevmode \kern.03em\raise.7ex\hbox{\the\scriptfont0 1}\kern-.2em
/\kern-.21em\lower.56ex\hbox{\the\scriptfont0 2}\kern.05em$, as do elec­trons, so a dif­fer­ence of one neu­tron switches the net atomic spin be­tween half-in­te­ger (he­lium-3) and in­te­ger (he­lium-4). That makes the he­lium-3 atom a fermion but the he­lium-4 one a bo­son. At ex­tremely low tem­per­a­tures it makes a big dif­fer­ence in be­hav­ior, chap­ter 11.

In terms of sym­bols, it is con­ven­tional to pre­cede the el­e­ment sym­bol by the mass num­ber as a su­per­script and the atomic num­ber as a sub­script. So nor­mal hy­dro­gen-1 is in­di­cated by ${}\fourIdx{1}{1}{}{}{\rm {H}}$, hy­dro­gen-2 by ${}\fourIdx{2}{1}{}{}{\rm {H}}$, he­lium-3 by ${}\fourIdx{3}{2}{}{}{\rm {He}}$, and he­lium-4 by ${}\fourIdx{4}{2}{}{}{\rm {He}}$.

Nu­clei with the same mass num­ber $A$ are called “iso­bars.” Yes, this con­flicts with the es­tab­lished us­age of the word iso­bar for lines of con­stant pres­sure in me­te­o­rol­ogy, but in this case physi­cists have blown it. There is not likely to be any re­sult­ing con­fu­sion un­less there is a nu­clear win­ter.

Some­times the el­e­ment sym­bol is also fol­lowed by the num­ber of neu­trons as a sub­script. How­ever, that then raises the ques­tion whether H$_2$ stands for hy­dro­gen-3 or a hy­dro­gen mol­e­cule. The neu­tron num­ber can read­ily by found by sub­tract­ing the atomic num­ber from the mass num­ber,

\begin{displaymath}
\fbox{$\displaystyle
N = A - Z
$}
\end{displaymath} (14.1)

so this book will leave it out.

It may also be noted that the atomic num­ber is tech­ni­cally re­dun­dant, since the chem­i­cal sym­bol al­ready im­plies the num­ber of pro­tons. It is of­ten left away, be­cause that con­fuses peo­ple who do not re­mem­ber the atomic num­ber of every chem­i­cal sym­bol in the pe­ri­odic ta­ble. To cre­ate fur­ther con­fu­sion, deu­terium is of­ten in­di­cated by chem­i­cal sym­bol ${\rm {D}}$ in­stead of ${\rm {H}}$. It is hi­lar­i­ous to see peo­ple who have for­got­ten this search through a pe­ri­odic ta­ble for el­e­ment ${\rm {D}}$. For ad­di­tional fun, the un­sta­ble hy­dro­gen-3 nu­cleus, with one pro­ton and two neu­trons, is also called the “tri­tium” nu­cleus, or “tri­ton,” and in­di­cated by ${\rm {T}}$ in­stead of ${}\fourIdx{3}{1}{}{}{\rm {H}}$. The he­lium-3 nu­cleus is also called the “he­lion.” For­tu­nately for us all, he­lion starts with an h.

Fig­ure 14.1: Chart of the nu­clides.
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...
...{X: given data less than 50\%}}}
\end{picture}}}}
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\end{figure}

Fig­ure 14.2: Nu­clear de­cay modes. [pdf][con]
\begin{figure}\centering
\setlength{\unitlength}{1pt}
\begin{picture}(405,56...
...{\makebox(0,0)[l]{$\fourIdx{4}{2}{}{}{\rm He}$}}
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\end{figure}

The nu­clei men­tioned above are just a tiny sam­ple of the to­tal of 256 nu­clei that are sta­ble and a much greater num­ber still that are ob­served but un­sta­ble. It is con­ven­tional to rep­re­sent both the sta­ble and un­sta­ble nu­clei in a Chart Of the Nu­clides, (CON), like the one shown in fig­ure 14.1. In the CON, the tiny green squares are the sta­ble nu­clei. Squares of col­ors other than green rep­re­sent un­sta­ble nu­clei. The hor­i­zon­tal po­si­tion of each square gives the num­ber of neu­trons $N$ (se­lected magic val­ues are listed along the hor­i­zon­tal axis). The ver­ti­cal po­si­tion gives the num­ber of pro­tons $Z$, (the cru­cial num­ber that de­ter­mines what chem­i­cal prop­er­ties an atom with that nu­cleus has). Note that $Z=82$ is lead, the last el­e­ment with at least one sta­ble nu­cleus. In fact, lead has four sta­ble iso­topes and nat­u­rally oc­cur­ing lead atoms have a fair chance of hav­ing any one of the four as nu­cleus. The fact that lead is so un­usu­ally sta­ble has a lot to do with the fact that lead is right on top of the $Z=82$ magic line, and close to the $N=126$ magic line. But more on that later.

Be­fore con­tin­u­ing the dis­cus­sion of the CON, a graph­i­cal prob­lem must be ad­dressed. While you can­not ar­gue about taste, 99.9% of read­ers would surely agree that 14.1 is (a) ugly as hell, and (b) re­quires a mag­ni­fy­ing glass to read. The Chart Of the Nu­clides is well suited for print­ing out on two yards of pa­per and hang­ing on the wall of your of­fice in its full glory. But in a book, it re­ally does not work. It could be made slightly big­ger if printed out side­ways, but ro­tat­ing a mon­i­tor with cof­fee cups on it and ca­bles at­tached is a bit awk­ward. And a crick in your neck is not that great ei­ther.

Based on these con­sid­er­a­tions, from now on, this book will no longer plot the neu­tron num­ber $N$ along the hor­i­zon­tal axis, but the “neu­tron ex­cess” $N-Z$. The neu­tron ex­cess is how many more neu­trons there are than pro­tons. That is an im­por­tant num­ber, maybe even more im­por­tant than the ab­solute num­ber of neu­trons. The cor­re­spond­ing mod­i­fied chart of the nu­clides is in fig­ure 14.2. It will be called the RE­CON (Re­vised Chart of the Nu­clei). It gives you some­thing you can view in com­fort.

But ad­mit­tedly there are some dis­ad­van­tages. In the RE­CON the iso­tones (the lines con­nect­ing nu­clei with the same num­ber of neu­trons) are no longer ver­ti­cal; now they slope down by 45$\POW9,{\circ}$. That can­not be helped. Sim­i­larly the iso­bars, the lines con­nect­ing nu­clei with the same to­tal num­ber of nu­cle­ons, no longer slope down by 45$\POW9,{\circ}$ like in the CON. In the RE­CON they slope down with the smaller slope 1/2: go­ing down one square to the pre­vi­ous chem­i­cal el­e­ment now re­quires that you go two squares to the right to stay on the same iso­bar.

So be it. The good news is that the neu­tron ex­cess is a lot more rel­e­vant to nu­clear sta­bil­ity than the ab­solute num­ber of nu­cle­ons. For ex­am­ple, at low val­ues of $Z$, the green band in RE­CON fig­ure 14.2 is ver­ti­cal, demon­strat­ing very clearly that in­deed for light nu­clei, the num­ber of neu­trons must be about equal to the num­ber of pro­tons. Also for heav­ier nu­clei, the RE­CON shows much more clearly ex­actly how much the rel­a­tive num­ber of neu­trons goes up to mit­i­gate the ef­fect of the Coulomb re­pul­sions be­tween pro­tons.

There is an other ad­van­tage to the RE­CON. It has to do with the fact that those nu­clei in which both the num­ber of pro­tons and the num­ber of neu­trons is even, the even-even nu­clei, are found to have en­hanced sta­bil­ity. On the other hand those nu­clei in which both the num­ber of pro­tons and the num­ber of neu­trons is odd, the odd-odd nu­clei, are found to have re­duced sta­bil­ity. Sim­ply put, pro­tons like to pair up, and so do neu­trons.

It works out that in the RE­CON, the even-even and odd-odd nu­clei end up on the same ver­ti­cal lines. (These ver­ti­cal lines al­ter­nate with ver­ti­cal lines of even-odd and odd-even nu­clei.) So wher­ever in fig­ure 14.2 you see a ver­ti­cal line with al­ter­nat­ing green and non-green squares, well, the sta­ble green squares are the even-even nu­clei and the non-green ones in be­tween the odd-odd ones. The pat­tern very con­vinc­ingly demon­strates that in­deed even-even nu­clei are a lot more sta­ble than odd-odd ones. (In the CON, the equiv­a­lent lines slant by 45$\POW9,{\circ}$ and are not by far as strik­ing.)

In the in­ter­me­di­ate ver­ti­cal lines in the RE­CON, where you do not see such a pe­ri­odic vari­a­tion of sta­bil­ity, you find the even-odd and odd-even nu­clei. Note that on these lines, the ver­ti­cal ex­tent of green squares is much less than on the ad­ja­cent lines with even-even nu­clei. This demon­strates graph­i­cally that even-even nu­clei are not just a lot more sta­ble than odd-odd ones; they are also a lot more sta­ble than even-odd and odd-even ones.

All this also makes it easy to fig­ure out whether a given nu­cleus is is even-even or odd-odd in the RE­CON. Look whether the ver­ti­cal line it is on has a se­ries of al­ter­nat­ing green and non-green squares; if so, then that is a line of even-even and odd-odd nu­clei. The ad­ja­cent two lines then con­tain even-odd and odd-even nu­clei. (In the re­gion of heav­i­est nu­clei, you can typ­i­cally look at the yel­low al­pha-de­cay nu­clei as a sub­sti­tute for the green nu­clei.) Al­ter­na­tively, if you see two green squares im­me­di­ately above each other in the RE­CON above $Z=8$, then that ver­ti­cal line con­sists of even-odd and odd-even nu­clei; there are no sta­ble odd-odd nu­clei above $Z=7$. (Con­versely, the RE­CON il­lus­trates that quite clearly too.)

Note also that the mass num­ber $A$ is odd on the even-odd, odd-even ver­ti­cal lines. And $A$ is even on the even-even, odd-odd ver­ti­cal lines. While the mass num­ber by iself does not have that much phys­i­cal mean­ing, nu­clear physi­cists of­ten use “odd mass num­ber nu­clei” as a short­hand for “even-odd and odd-even nu­clei.”

If you are re­ally a CON man or woman, there is noth­ing wrong with that. You can al­ways click on the [con] link pro­vided in the leg­end of the fig­ure to load the fig­ure in CON for­mat as a sep­a­rate pdf file. Con­versely, if you re­ally like the RE­CON for­mat and you want to print it and hang it on your wall, click on the [pdf] link in­stead for a print­able ver­sion. And ei­ther type of pdf can be read­ily mag­ni­fied to see de­tails more clearly.

Let's look at some of the de­tails of RE­CON fig­ure 14.2. The left­most green square in the bot­tom row ($Z=1$) is the hy­dro­gen-1 nu­cleus, and the green square im­me­di­ately to the right of it is hy­dro­gen-2, deu­terium. The green squares on the sec­ond-low­est row ($Z=2$) are he­lium-3 and he­lium-4 re­spec­tively.

Like in the CON, iso­topes are found on the same hor­i­zon­tal line in the RE­CON. As men­tioned, the hor­i­zon­tal po­si­tion of each square in RE­CON fig­ure 14.2 in­di­cates the neu­tron ex­cess. For ex­am­ple, hy­dro­gen-2 and he­lium-4 both have equal num­bers of pro­tons and neu­trons. So they are at the same hor­i­zon­tal po­si­tion, zero, in the fig­ure. Sim­i­larly, hy­dro­gen-1 and he­lium-3 both have a neu­tron ex­cess of mi­nus one. The fig­ure shows that sta­ble light nu­clei have about the same num­ber of neu­trons as pro­tons. How­ever, for the heav­i­est nu­clei, there are about 50% more neu­trons than pro­tons. For heavy nu­clei, too many closely packed pro­tons would mean too much Coulomb re­pul­sion.

Many iso­topes are un­sta­ble and de­cay spon­ta­neously, lib­er­at­ing en­ergy. For ex­am­ple, con­sider the blue square to the right of ${}\fourIdx{2}{1}{}{}{\rm {H}}$ in fig­ure 14.2. That is ${}\fourIdx{3}{1}{}{}{\rm {H}}$, hy­dro­gen-3 or tri­tium. It is un­sta­ble. Af­ter on av­er­age about twelve years, it will turn into he­lium-3. In par­tic­u­lar, one of the two neu­trons turns into a pos­i­tively charged pro­ton. So there are still three nu­cle­ons, the mass num­ber has stayed the same, but the atomic num­ber has in­creased one unit. In terms of RE­CON fig­ure 14.2, the nu­cleus has changed into one that is one place up and two places to the left.

Since charge is con­served, the cre­ation of the pos­i­tive charge can only hap­pen if the neu­tron emits a com­pen­sat­ing neg­a­tive charge; the neu­tron does so by emit­ting an elec­tron. For his­tor­i­cal rea­sons, a de­cay process of this type is called beta de­cay ($\beta$-​de­cay) in­stead of elec­tron emis­sion; ini­tially it was not rec­og­nized that the ob­served ra­di­a­tion was merely high en­ergy elec­trons. And the name could not be changed later, be­cause that would add clar­ity. (An an­ti­neu­trino is also emit­ted, but it is al­most im­pos­si­ble to de­tect: so­lar neu­tri­nos will read­ily travel all the way through the earth with only a minis­cule chance of be­ing cap­tured.)

Nu­clei with too many neu­trons tend to use beta de­cay to turn the ex­cess into pro­tons in or­der to be­come sta­ble. Fig­ure 14.2 shows nu­clei that suf­fer beta de­cay in blue. Since in the de­cay process they move to­wards the left, they move to­wards the sta­ble green area. Al­though not shown in the fig­ure, a lone neu­tron also suf­fers beta de­cay af­ter about 10 min­utes and so turns into a pro­ton.

If nu­clei have too many pro­tons rather than too many neu­trons, they can turn their ex­cess pro­tons into neu­trons by emit­ting a positron. The positron, the anti-par­ti­cle of the elec­tron, car­ries away one unit of pos­i­tive charge, turn­ing a pos­i­tively charged pro­ton into a neu­tral neu­tron.

How­ever, a nu­cleus has a much eas­ier way to get rid of one unit of net pos­i­tive charge: it can swipe a neg­a­tively charged elec­tron from the atom it is in. This is called elec­tron cap­ture (EC). An elec­tron neu­trino is emit­ted in this process.

Elec­tron cap­ture is also called K-cap­ture of L-cap­ture, de­pend­ing on the elec­tron shell from which the elec­tron is swiped. It is also re­ferred to as in­verse beta de­cay, es­pe­cially within the con­text of “neu­tron stars.” These stars are so mas­sive that their atoms col­lapse un­der grav­ity and the elec­trons and pro­tons com­bine into neu­trons. These stars then emit enor­mous amounts of high-en­ergy neu­tri­nos, tak­ing along a large amount of the avail­able en­ergy of the star.

Of course, in­verse beta de­cay is not re­ally in­verse beta de­cay, be­cause in beta de­cay the emit­ted elec­tron does not go into an empty atomic or­bit, and in beta de­cay no neu­trino is ab­sorbed; in­stead an an­ti­neu­trino is emit­ted.

Positron emis­sion is also of­ten called beta-plus de­cay ($\beta^+$-​de­cay). Af­ter all, if you do have ob­so­lete ter­mi­nol­ogy, it is fun to use it to the fullest. Note that NUBASE 2003 uses the term beta-plus de­cay to in­di­cate ei­ther positron emis­sion or elec­tron cap­ture. In anal­ogy with the beta-plus ter­mi­nol­ogy, elec­tron emis­sion is also com­monly called beta-mi­nus de­cay or nega­tron emis­sion. Some physi­cists leave the r away to save trees and talk about posi­tons and nega­tons.

The nu­clei that suf­fer beta-plus de­cay or elec­tron cap­ture are shown as red squares in fig­ure 14.2. In the de­cay, a pro­ton turns into a neu­tron, so the nu­cleus moves one place down and two places to­wards the right. That means that these nu­clei too move to­wards the sta­ble green area.

There are a va­ri­ety of other ways in which nu­clei may de­cay. If the num­ber of pro­tons or neu­trons is re­ally ex­ces­sive, the nu­cleus may just kick out one of the bums in­stead of con­vert it. Nu­clei that do that are marked with P,” re­spec­tively “N in fig­ure 14.2,

Sim­i­larly, heavy nu­clei that are weak­ened by Coulomb re­pul­sions tend to just throw some nu­cle­ons out. Com­monly, a ${}\fourIdx{4}{2}{}{}{\rm {He}}$ he­lium-4 nu­cleus is emit­ted, as this is a very sta­ble nu­cleus that does not re­quire much en­ergy to cre­ate. Such an emis­sion is called “al­pha de­cay” ($\alpha$-​de­cay) be­cause he­lium-4 emis­sion would be eas­ily un­der­stand­able. Al­pha de­cay re­duces the mass num­ber $A$ by 4 and the atomic num­ber $Z$ by 2. The nu­cleus moves two places straight down in RE­CON fig­ure 14.2.

If nu­clei are re­ally over­sized, they may just fall apart com­pletely; that is called spon­ta­neous fis­sion.

An­other process, “gamma de­cay,” is not shown in fig­ure 14.2. In gamma de­cay, an ex­cited nu­cleus tran­si­tions to a lower en­ergy state and emits the re­leased en­ergy as very en­er­getic elec­tro­mag­netic ra­di­a­tion. This is much like the spon­ta­neous de­cay of ex­cited elec­tron lev­els in atoms, which too re­leases elec­tro­mag­netic ra­di­a­tion. How­ever, the elec­tro­mag­netic ra­di­a­tion emit­ted in gamma de­cay is much more pow­er­ful than that emit­ted by atomic elec­trons, as nu­clear en­er­gies are so much higher than those of atomic elec­trons. Un­like the de­cays shown in fig­ure 14.2, in gamma de­cay the type of nu­cleus does not change; there is no change in the num­ber of pro­tons nor neu­trons.

Un­like gamma de­cay, the nu­clear de­cays shown in fig­ure 14.2 are from their their non-ex­cited “ground state.” But the shown de­cays are com­monly as­so­ci­ated with ad­di­tional gamma ra­di­a­tion, since the de­cay tends to leave the changed nu­cleus in an ex­cited state.

Gamma de­cay as a sep­a­rate process, not di­rectly caused by an­other process, is of­ten re­ferred to as an “iso­meric tran­si­tion” (IT) or “in­ter­nal tran­si­tion.” In nu­clear physics, an iso­mer is a long-lived ex­cited state of a nu­cleus.

Be­sides gamma de­cay, a sec­ond way that an ex­cited nu­cleus can get rid of ex­cess en­ergy is by throw­ing an elec­tron from the atomic elec­tron cloud sur­round­ing the nu­cleus out of the atom. You or I would prob­a­bly call that some­thing like elec­tron ejec­tion. But what bet­ter name for throw­ing an elec­tron, that is al­ready out­side the nu­cleus to start with, com­pletely out of the atom than in­ter­nal con­ver­sion (IC)? It can pro­duce some of that hi­lar­i­ous con­fu­sion with the sim­i­lar sound­ing term in­ter­nal tran­si­tion. In­ter­nal con­ver­sion is usu­ally in­cluded in the term iso­meric tran­si­tion.

Fig­ure 14.2 mixes col­ors if more than one de­cay mode oc­curs for a nu­cleus. The dom­i­nant de­cay is of­ten im­me­di­ately fol­lowed by an­other de­cay process. The sub­se­quent de­cay is not shown. Data are from NUBASE 2003, with­out any later up­dates. The blank square right at the sta­ble re­gion is sil­ver-106, and has a half-life of 24 min­utes. Other sources list it as de­cay­ing through the ex­pected elec­tron cap­ture or positron emis­sion. But NUBASE 2003 lists that con­tri­bu­tion as un­known and only men­tions that beta-mi­nus de­cay is neg­li­gi­ble.


Ta­ble 14.2: Al­ter­nate names for nu­clei.
\begin{table}\begin{displaymath}
\begin{array}{ccccccccc}
\hline\hline
\mbox{...
...0}{84}{}{}{\rm Po} \\
\hline\hline
\end{array} \end{displaymath}
\end{table}


Since so many out­siders know what nu­clear sym­bols mean, physi­cists pre­fer to use ob­so­lete names to con­fuse them. Ta­ble 14.2 has a list of names used. The ab­bre­vi­a­tions re­fer to his­tor­i­cal names for de­cay prod­ucts of ra­dium (ra­dium em­a­na­tion, ra­dium A, etc.)


Key Points
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Nu­clei con­sist of pro­tons and neu­trons held to­gether by the nu­clear force.

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Pro­tons and neu­trons are col­lec­tively re­ferred to as nu­cle­ons.

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Pro­tons also re­pel each other by the Coulomb force.

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The num­ber of pro­tons in a nu­cleus is the atomic num­ber $Z$. The num­ber of neu­trons is the neu­tron num­ber $N$. The to­tal num­ber of nu­cle­ons $Z+N$ is the mass num­ber or nu­cleon num­ber $A$.

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Nu­clei with the same num­ber of pro­tons $Z$ cor­re­spond to atoms with the same place in the pe­ri­odic ta­ble of chem­istry. There­fore nu­clei with the same atomic num­ber are called iso­topes.

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To pro­mote con­fu­sion, nu­clei with the same num­ber of neu­trons $N$ are called iso­tones, and nu­clei with the same to­tal num­ber of nu­cle­ons $A$ are called iso­bars.

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For an ex­am­ple nu­clear sym­bol, con­sider ${}\fourIdx{4}{2}{}{}{\rm {He}}$. It in­di­cates a he­lium atom nu­cleus con­sist­ing of $A=4$ nu­cle­ons, the left su­per­script, of which $Z=2$ are pro­tons, the left sub­script. Since it would not be he­lium if it did not have 2 pro­tons, that sub­script is of­ten left away. If you do not re­mem­ber $Z$ for, say, ${}\fourIdx{146}{}{}{}{\rm {Pm}}$, you can look it up in a pe­ri­odic ta­ble, like 5.8. But avoid do­ing so with el­e­ments $D$ and $T$.

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Since these rules are too sim­ple, physi­cists of­ten drag up ob­so­lete sym­bols like RE” and “RaF from the dark his­tory of nu­clear physics. You can look these up in a ta­ble above.

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The name for the nu­cleus with sym­bol ${}\fourIdx{4}{2}{}{}{\rm {He}}$ is he­lium-4, where the 4 is again the num­ber of nu­cle­ons $A$.

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An odd mass num­ber $A$ cor­re­sponds to ei­ther an even-odd nu­cleus, a nu­cleus in which the num­ber of pro­tons is even and the num­ber of nu­cle­ons odd, or to an odd-even nu­cleus, in which it is the other way around. An even mass num­ber $A$ cor­re­sponds to ei­ther an even-even nu­cleus, which tends to have rel­a­tively high sta­bil­ity, or to an odd-odd nu­cleus, which tends to have rel­a­tively low sta­bil­ity. The ver­ti­cal columns in a RE­CON plot cor­re­spond al­ter­nat­ingly to odd and even mass num­bers $A$. The two types of columns look very dif­fer­ent.

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Nu­clei can de­cay by var­i­ous mech­a­nisms. To pro­mote con­fu­sion, emis­sion of a he­lium-4 nu­cleus is called al­pha de­cay or $alpha$ de­cay. Emis­sion of an elec­tron is called beta de­cay, or $\beta$ de­cay, or beta-mi­nus de­cay, or $\beta^-$ de­cay, or nega­tron emis­sion, or nega­ton emis­sion, but never elec­tron emis­sion. To do the lat­ter would be se­verely frowned upon by physi­cists. Emis­sion of a positron (posi­ton) may be called beta-plus de­cay, or $\beta^+$ de­cay, but ei­ther term might be used to also in­di­cate elec­tron cap­ture (EC), de­pend­ing on who uses the term. Elec­tron cap­ture may also be called K-cap­ture or L-cap­ture or even in­verse beta de­cay, though it is not. More ex­treme de­cay mech­a­nisms are pro­ton or neu­tron emis­sion, and spon­ta­neous fis­sion. Kick­ing an elec­tron in the elec­tron cloud out­side the nu­cleus com­pletely free of the atom is called in­ter­nal con­ver­sion. Mere emis­sion of elec­tro­mag­netic ra­di­a­tion is called gamma de­cay or $\gamma$ de­cay.

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No, this is not a story made up by this book to put physi­cists in a bad light.