On neutron-deficient isotopes of light nuclei and the phenomena of proton and two-proton radioactivity

1.E-~.

Nuclear Physzcs 19 (1960) 4 8 2 - - 4 9 5 ,

~5

No~th-Holla~M I'ltbll~hlJz~ ¢o. .q.t,h'~dam

Not to be reproduced by photoprmt or mtelotlhn wlthotlt written pertmsslon from th~ publlsh, t

ON NEUTRON-DEFICIENT ISOTOPES OF LIGHT NUCLEI AND THE PHENOMENA OF PROTON AND TWO-PROTON RADIOACTIVITY V I GOLDANSKY

P N Lebedev Phvswal Instdute, Ub'SR Aca'lemv ofSc2e~ces, 3Io~cow R e c e i v e d 14 M a r d l

1960

A b s t r a c t : A p p l i c a t i o n of i s o b a r i c l n v a r i a n c e p r i n c l p h , s t o l i g h t nuclei l e a d s t o a v e r y r u m p l e r e l a t i o n b e t w e e n t h e Z - t h p r o t o n b i n d i n g e n e r g y E p ill n u c l e u s 1 ( g M N A) a n d t h e Z - t h n e u t r o n b i n d i n g e n e r g y E n i n t h e m i r o r n u c l e u s 2 (NMZ A) W i t h a n a c c u r a c y of t h e o r d e r of a f e w p e r c e n t t h e i r d i f f e r e n c e En2 - E p l - - - ] E n p is i n d e p e n d e n t of N f o r a g i v e n Z a n d is gix e n b y _ _ Z_ _- - - 1

2Z

AEnp ~ En(zMz ) - - Ep(zNI~Z) ~ 1 2 ( 2 Z - - 1 ) ~ ' w h i c h is m o r e c o r r e c t t h a n t h e u s u a l e x p r e s s i o n 1 2 ( Z - - I ) / ( Z -4- N 1)~- B y e x p l o i t i n g this fact one can predict the existence and properties of almost ninety new neutron-deficient i s o t o p e s of l i g h t n u c l e i ( u p t o Z = 34) a n d e s t a b l i s h t h e l i m i t s of s t a b d i t y of t h e i s o t o p e s w i t h r e s p e c t t o d e c a y w i t h p r o t o n e m i s s i o n A m o n g t h e s p e c i f i c p r o p e r t i e s of n e u t r o n - d e f i c w n t I s o t o p e s , p r o t o n a n d t w o - p r o t o n r a d i o a c t i v i t y e f f e c t s w h i c h m a y o c c u r a r e of s p e c i a l i n t e r e s t Some nuclei are indicated in which these effects may be observed The mare features of a very curious phenomenon of two-proton radioactivity are discussed

1. Fundamental Energy Relations As is well known, the difference in the neutron and proton binding energies in neighbouring mirror nuclei z-1M~ and zMzA_ 1 equals the proton Coulomb energy 1.2 ( Z - 1)/(A - - 1)¢ MeV. At first glance it would seen that the corresponding difference between the Z-th neutron binding energy in a nucleus 2, En(NM~), for which the condition N = Z - - 1 does not hold, and the Z-th proton binding energy in the mirror nucleus 1, Ep(zM~), should equal the Coulomb energy of the Z-th proton in nucleus 1, which is m 1.2 ( Z - - I)/(Z + N - - I)~, i.e. it should depend not only on Z but also on N (and hence on A). It can readily be shown, however, that if the isobaric invariance principle is applied, the quantityAEnp under consideration is defined by the following relation*: f A n o t h e r s i m p l e c o r o l l a r y ot isobaric l n v a r i a n c e p r i n c i p l e s is, as c a n be r e a d i l y p r o v e d , t h e f o l l o w i n g r e l a t i o n c h a r a c t e r i z i n g t h e m a s s difference b e t w e e n r e m o t e m i r r o r nuclei ~ llere

,4 Z~'[N-

A (Z-- N) A M 0 , NMZ ~-

A [ ~ A ~ ½ M ~.a

A : ~ - - { A - - ½ M {A±*t- - 4kA--I~V['}A + 1 }

I n s o m e c a s e s t h i s f o r m u l a m a y be useful a n d e \ e n ( m p l o y e d liy us in this w o r k 482

foroddA

,

for e v e n .q

m o r e c o n v e n i e n t t h a n t h e r e l a t i o n (2~

ON NEUTRON-DEFICIENT

483

ISOTOPES

AE°p E.(NM) --Ep(zM ) ---- [Ecou,(zM~)

~l.2,Z--1 [

A~

-- Eco.,(z-,MNa - t )j, -- [Eco.,(NM~) -- Eco.,(NM~2 I)] [ 1 1 ]t ½(Z - - N - - 1 ) (A - - 2)

(A--l)

+

.4~ / '

(1)

and to within a few per cent is in general independent of N. For Z < N as well as Z > N, one has also where

AE.p ~ AEo ~ E.(zM~ z) - - Ep(zM~Z) ,

(2)

Z--1 AN o ~ 1.2 ( 2 Z - - 1) +'

(3)

Besides the usual first two terms in squared brackets, account has also been taken in (1) of the change in the Coulomb energy due to decrease of the size of the nucleus as a result of the removal of a neutron (the last two terms in squared brackets). Since a uniform distribution of the nuclear charge is a rough approximation, especially for light nuclei, relation (3) becomes correct with sufficient accuracy (not worse than ~ 10 %) for Z ) 6. Relation (2), on the other hand, is satisfactorily fulfilled for all values of Z, as can be seen from the experimental data presented in fig. 1 on AE.p and AEo for nuclei up to scandium. Only two 1

2

3

4

. 5 . 6 . 7 . 8 . 9 10

. 11 ) 2

,13 ,14 .15 16 17 ,18 .19 , 2 0 2 1

H1 He 2 ~76

/V

LI 3

142

Be 4

191

B5

233

C (5

273

N7

!

310

0 8 F" g

345 !

37g

N.,O

Na 11 Mg12

,,o

~_~

440 ~

470

A113

4 98

S114

5 26

P 15

554

S 16

580

C117

605

At18

632

K19

656

20

680

Sc 21

704

Ca

Difference of binding energy of Z-th neutron m a N M z a nucleus and binding energy of Z-th proton m a z M n A nucleus (the numbers m the small squares are the values of AEnp ).

F i g , 1.

7

3ulphur

2hlqrlne

7

Phosphorus

~lhcon

12 4

51 >56 106

15 5

185 <5.5

II

14

16

--52

--(<~ 12 7) 18

~4

12

5

O3

04

ll 6 ;>42 109

17 13 ~2 94 12 97

10.5

15.2 <61

7)

001 depends )n F 16 level< 0O5

' d e p e n d s on N 16 levels

~>ool

~01

~'½~ (sec}

9 9)

34

17 11--: 24

<45

12

17

17

14 5

<16

< 194

>46

<134

28

E B (MeV)

[21

11 ( < 12 4) 75

14 13

:8

!31 !7 [79

8

~lagneslum

!14

05--18

14

--25 - - ( < 2 1)

--36 --(< 13)

>15

1154-05 ~04± 4 ~75

I03

- - 1.6

En (MeV)

> 1.7

Ep tMeV)

!944-0 161~3

286 < 38 3 273 27 7 - - 2 9

< <

<

<

.'t (MeV)

--03

2 7 8 6

8

M-

!83

2 2 0

8

V

~odium

geon

gitrogen 3xygen

Beryllium Boron 2arbon

Helium

glement

6

Z

S u m m a r y of t h e predicted isotopes a n d their properties

TABLE 1

Questionable in ref a)

~ u e s t i o n a b l e in ref a) T½# refers to t r a n s i t i o n to ~+ level )f S127 (0 9 MeV) F½# for t r a n s i t i o n to 1 5 MeV evel in p2s Predicted in ref a) F½# for t r a n s i t i o n to ~+ level .n p29 (1 4 MeV) Predicted in ref a) T½# for Lransltlon w i t h z l T - 0

~)

Questionable in ref a) T i p refers to t r a n s i t i o n to ½ level )f F 17 (31 MeV) ~Duestlonable in ref a) T½# refer~ to t r a n s i t i o n to {+ level n Ne 19 (02 MeV) Predicted in ref 4) Predicted in ref a) T½# refers to t r a n s m o n to 1+ evel of A124 (0 5 MeV) Predicted in ref 3)

~redlcted in ref 4) (fl-)

T½# refers to t r a n s i t i o n to 3 2 kleV level of L18 (1 +) Also see cefs 4,5) [fl-) Predicted in ref 4) ( f l )

Xlote

ON NEUTRON-DEFICIENT ISOTOPES

485

~°

~ o o~

o~°~°~

~

~.8~ O

~

~°

~11

V

VV

v

~

V

VA

A

V

A

A

AI

I

AA

I

II

v

V

I

AIII

I

I

I IA

V

V

I I r V

I

i I

I I F

486

\

V

I GOLDANSX~

VVVVVV

VVV

VV VVVVV

V

V

VV

V

c~

i!l

I

I

-T

i

--i i

r ' !

PIIrr

, ! : '7

I

F ' #

m

J ,~ J i

,' I r I ~

I

r I

r I I

168

19

-44 --18

49 34 3 25 5 159 34 6 24 36 45 4

66 65 66

67 67 68

69

70

29 30

30

30

Rubldmm

Strontmm

Yttrmm

Zirconium

37

38

39

40

--34 15 --05

07 --44 --34

19

18

172

18

163

169

--21 --06 --04

223 145

2

Krypton

--

197 160

--33 --22

36

30

20 15

0.8 07 09

---3

--

--22 --19 --08 --05

167 184 148 157

155

36 ---3

65 64 65

64

--117 25 3 141 65

147 3.2 --33

--255 145 6.3 --37 --10 --174

1

19 23

(148) 0 5 5)

( < 01) <01 <01

(17 4) 122 131

( < 0 05)

~< o 1)

( < 0 1) ( < o l)

~01

(% 0 1) ( < 0 1)

(14 5) 157

--01

<01 ( < 01) <0.1 <01 <01 <01

14.2 (17 8) 13 144 95 101

<01

132

20 1 158 182 136

---08 05

Bromine

27 28 29

30 26 27 28 29 30

-295 156 39 -35 --132 --184

61 57 58 59 60 61

30 25 26 27 28 29

07

35

Selenmm

Arsemc

Germanmm

- -237

bO

29

I s o t o p e s beginning from .4 -- 81 k n o w n a t p r e s e n t I s o t o p e s beginning from A = 82 k n o w n at present I s o t o p e s beginning from A = 86 k n o w n at p r e s e n t

I s o t o p e s beginning from .4 = 81 k n o w n at present

I s o t o p e s beginning from ,4 = 76 k n o w n at p r e s e n t

Isotopes beginning from A =- 73 k n o w n at p r e s e n t

H i t h e r t o undiscovered asotopes with A ~ 65-69 also stable

I s o t o p e s wzth ,4 = 64-67 also evidently stable

Hxtherto undiscovered Isotopes x~lth A = 63-65 also stabl~

H i t h e r t o undmcovered tootopes with .4 = 6 2 63 also stable

4~

0

O

+

O

O Z Z

488

~

I GOLDANSKY

significant deviations from (2) (for the pairs F2°-Na 2° and Ne21-Na 21) are observed. The discrepancies are evidently due to the fact that the mass defect value of Na 2° presented in ref. 1) (see also ref. 2)) is too high by about 1.5 MeV (it should be 12.7 MeV), as a result of a very rough estimation of the end point energy of the/~-spectrum.

2. Neutron-deficient Isotopes By applying (2) and, in those cases when A E o is unknown, by applying (3), one can predict the properties of a large number of neutron-deficient isotopes 2

4

6

8

~0

~2

~4

,6

,8

20

22

24

26

28

3o

32

34

36

2 ---- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4~-;

°f:;tl I f I

16

I I I+++-(~)-

[++'+-

,8

+1

20

++!

I f I I +1 I

24

Z"

,-®-,

I J

22

++1

I f : '1+?+9+-(+) +-~? -Q +++ ~ +-'4:/4-+++ 9 +'--'~4-[~++ 9 + l/ [ 14+++-(,~-

/

+++ ?@-

I I I

+++++-9

26

4-

28 30

+ + +

32 34

I I

] +

3a 40

[

If

++4 I++++ /

1+4

++

I. +1

I l

46

N

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

]'t"+94

J++9,

+1

,~2

50

9 ~++9+ 9(:F)-9 ++++ 9 :l:-+ +++?+-+ + +- + + 9+/?' 4 "

L+I i II

44

4e

+-9+ ? + _(~)_ 9--

i Ll115++9 + + 9_-(~)-

I I ++

+1

,36

38

I

I I ]

I [

F i g 2 D a t a o n k n o w n a n d p r e d i c t e d I s o t o p e s T h e r e g i o n of p r e v m u s l y k n o w n I s o t o p e s is o u t h n e d . T h e m e a n i n g of t h e d i f f e r e n t s y m b o l s ~s + p r e d i c t e d i s o t o p e s s t a b l e w i t h r e s p e c t t o p a n d n emlssmn; ? p-stablhty questmnable, O 2p-activity possible, -- isotopes which beyond doubt are unstable with respect to n or p emissmn

ON NEUTRON-DEFICIENT

4.89

ISOTOPES

of light nuclei on the basis of known properties of the corresponding mirror nuclei with surplus neutrons. Some predictable properties are the neutron and proton binding energies, mass defects,/~-decay half-periods and mechanism of the decay (transition to the ground or excited states), possibility of observing proton or two-proton radioactivity. A summary of all predicted isotopes (including proton-unstable ones), and their properties is presented in table 1 and fig. 2. Isotopes whose existence have been previously predicted b y Baz 3) or Zeldovich 4) are correspondingly designated. The values of ( M - A), Ep, E, and E~ presented in the table are correct within an accuracy of 1 MeV. The values of T+p should be regarded as order of magnitude values. The accuracy of the energy values was such that it was meaningless to take into account in the numerical calculations corrections for the increase of nuclear dimensions with the rise of Z at given A or for the proton Coulomb exchange energy of the type considered, for example, in ref. ~). With account of these corrections we obtain

AE,p = =

E,(NMaz) - - Ep(zM~)

[Ecou,(zM ) --Ecou,(z-tMN

)] _ [Ecou,(NM~)__ Ecou,(NMz_ A-11)]

= 0.6 [(Z - - N) (Z + N) + - ( Z - 1 - N ) ( Z - 1

--0.6

Z+ CZ(z+N)+ N+

--CN(z+N)

(Z-

+N) + ]

+ +CN(Z+N-1)

where

1)+

Cz-,(Z__l N+

+ N ) +]

+ '

(4)

Cm -= 0 . 7 6 3 6 - e -°'38 ~

(5)

It should be noted that to a large extent the correction terms compensate each other. With an accuracy of a few percent, 4 1 AEnp ~ 0.6 (2Z - - 1) + - -

CzZ+ 3Z

3(Z + N) (Z + U - 1)+

and, owing to the insignificant role of the correction, one can express the form

AE,p~_,O.6

(2Z--l) +-c

z~

~0.6[(2Z--1)

l-Cz]

(6)

AE,p in (7)

by assuming that N m Z in the correction term. It is easy to verify that corrections for Coulomb exchange interaction of the protons decreases AE,v with respect to (1), (2) or (3) by less than ~ 0.4 MeV.

490

v i GOLDANSKY

3./~-Decay The data presented in the table require some additional explanation which will be now given. In the mass defect calculations based on the nucleon binding energies computed from (2) and (3), use was made of the data presented in the summary tables in ref. l) and 5). Besides neutron-deficient isotopes some isotopes with an excess of neutrons are presented at the beginning of the table. Data pertaining to these isotopes were derived from information on the pairing energy of neutrons in neighbouring isotopes with even value, c)f Z (see ref. 5)). The properties thus derived were then employed to supplement the mum list of neutron-deficient isotopes by the corresponding mirror nuclei. The/3+ decay energies refer to a ground state transition. These energies are related to similar/3- transitions in mirror nuclei by the simple relationship E~+(zM~) - - Ep-(NM~) ~ 1.2

I

(2N--

17 + (2Z--

1)+ - - 2.6 ~ e ~ ~

(8)

(where 2.6 MeV ~ 2m~ + 2 ( m ~ - mH). In the calculations of the half-period for/3+-decay one should keep in m md the possible existence of "super-allowed" transitions not involving a change of isobaric spin. In such transitions Z r 1 3 I NA ~

*A Z~IN+ 1

the/3+ decay energy is given slmt,ly as E~+(AT = (,) ~ 1.2 ~Z- - - 1.8 MeV

(9)

A¢ (where 1.8 MeV = 2m~ + m. - - mH) and vanes slowly with A for a fixed value of Z. If E ~ exceeds the threshold defined by (9), the "super-allowed" transitions begin to compete with transition:, to the ground state, the rate of transitions with A T = 0 increasing with increasing Z as a result of the increase of their energy. Many of the neutron-deficient isotopes predicted here (practically all of them beginning at Z ~ 20) sh~,uld undergo/3+-decay with A T = 0 and subsequent cascade emission of y-quanta or of delayed protons (or couples of protons). In such cases the valueq of Ep presented in table 1 characterize the sum of the maximum positon em,rgy and energies of the subsequent 7-transitions. The peak positon energies for "super-allowed" transitions vary from 5 MeV for calcium to ~ 8 MeV for selenium and the half periods (for log ft ~ 3.5) change from ~ 0.5 to ~ 0.07 sec. The values of the lifetimes of a number of known /3+ active isotopes with Z = 1 3 - - 2 5 for which E p > 1 . 2 Z / A + - - 1 . 8 MeV (e.g. A1z4, Ca 3s, V 46 and Mn s°) confirm this assumption. Because of the low value of the energy, "super-allowed" transitions are

ON N E U T R O N - D E F I C I E N T

ISOTOPES

491

found to be quite slow for lighter nuclei and hence transitions to ground states more frequently become dominant. For such light nuclei the half-lives were mainly computed on the basis of available data on "mirror"/3- decay.

4. Proton Radioactivity The following is a list of stable isotopes which are located, according to our estimations, on the boundary of stability with respect to proton emission:

Li 6, Be 7, Bs, C9, N12, O13, F17, NOT, Na2OOg~), Mg19Os?), A123, Si2~(22~), p27, $26, C131, Ar 3o, K35, Ca35O47), Sc4O(39~), Ti 39, V43(42~), Cr43, Mn 46, Fe 4s, Co5O(4S~), Ni4S, Cu54, ZnSS(54~), Ga6O(Sg?), Ge59, AS64(0, Se62(610. A comparison of this list with that of isotopes known at present indicates that approximately ninety new neutron-deficient isotopes of light nuclei m a y yet be discovered. The next problem we consider is that regarding the possibility of detecting proton radioactivityT). It can easily be shown that the probability of observing this process is quite small. In fact, if the half life for p-decay IS less than 10 - 4 _ 10-3 sec it should already be difficult to record the events by delay coincidence techniques under the conditions of an accelerator. On the other hand, if the lifetime with respect to p-decay exceeds 1-10 sec the effect will be strongly obscured by/3+-decay. The half-life of proton-radioactive isotopes can approximately be determined from the formula log T~ (sec) ~ 0.43 Z ~ J ( x )

- - 22,

(10)

where x is the ratio of the emitted proton energy to the height of the Coulomb barrier: for x ~. 1 we have . / ( x ) --- 0.6x -~ [are cos x * - - x ~ (1 --x~)] ~ 0.6 [[:rx -~ ~ 2 1 •

(11)

For the ipterval T~ = 10 - - 10 -4 see the corresponding energies of the emitted protons are 0 . 0 3 - - 0 . 0 4 MeV (for Z----- 10), 0 . 1 - 0.15 MeV (for Z = 20), 0.2 - - 0.3 MeV (for Z = 30) and 0.35 - - 0.5 MeV (for Z = 40). The energy range of recorded proton radioactivity events, however, can be appreciably broadened by observing the emission of delayed protons occurring after reactions on photographic emulsion or cloud chamber vapors nuclei. If protons with a lag of ~ 10 -~2 sec are assumed to be distinguishable under such conditions from instantaneous protons, the upper limit for the energy of observed radioactive p-decays will increase up to 0.35 MeV (Z = 20), 0.70 MeV (Z = 30) and 1.1 MeV (Z = 40). Of course the accuracy of our calculations of the masses is much too small to permit us to predict whether proton radioactivity will be observed at all, not speaking of predicting in exactly which isotopes it should be observed. The only

492

v I GOLDANSKY

thing that is clear is that this phenomenon should be sought near the aforementioned stability boundaries (which is also true for some heavier nuclei not considered by us here).

5. Two-Proton Radioactivity Owing to the very large neutron binding energy for all isotopes considered here the latter will all be stable with respect to ~-decay from the ground state. However, a very curious effect, the two-proton radioactivity, can now be observed. Even at a positive proton binding energy instability with respect to emission of two protons may appear in even-Z isotopes. A well-known example s) of such two-proton instability is Be 6, but in this case the energy of Be 6 -~ Li 5 + p decay is less than the half width of the ground state of Li 5 and therefore the decay of Be 6 cannot be treated as two-proton radioactivity. The general condition for two-proton radioactivity is that the positive binding energy of the first proton must be larger than the half width of the emission of the second one. Therefore, the two-proton radioactive decay should be distinguished from possible p/3+- or p-decay chains, e.g. Zr6~

P

+ y68_

P

_~ S r 6 ~

P

÷ Rb66

ys9

P

+ Sr68

P

~ Rbe7

P

~Kr66__

P

_~ K r 6 5

R b 8~

P

__~ B f64 _ _ _ P -

~ S C 63

. ÷Se64

though in the p-decay chains the possibility of two-proton emission may essentially decrease the lifetime of p-radioactive isotopes with even Z = 2 m + 2 m those rare cases when the energy of 2p-decay Epp(2m + 2 ~ 2m) > 8Ep(2m + 2 ~ 2m + 1) . Variants of two-proton emission are illustrated in fig. 3(a, b, c), fig. 3c representing the "pure" case of two-proton radioactivity. Thus, in such isotopes which are stable against proton and alpha decay, two-proton decay m a y be observed. This effect, which can also be conveniently observed with photographic emulsions of in the cloud chamber m a y occur in Ne 16, Mg1708~), Si21(220, $ 2 s ( 2 4 0 , A r 2 9 ( 2 8 0 , Ca2S(24,), T p 8 , C r 42, Fe44(43), Ni46(47~), ZnS3(s4'), GeSg(Sa,), Se63~62,), Kr67(66,). The probability for simultaneous sub-barrier emission of two protons includes the product of the two barrier penetration factors for the protons or the product of the penetration factor for a doubly charged particle and a preexponential factor which characterizes the probability for two-proton correlation in the nucleus. The lifetimes of the Isotopes, therefore, assume values

ON NEUTRON-DEFICIENT ISOTOPES

493

convenient for measurement, which lie in a much broader energy interval in the case of two-proton decay than in the case of proton radioactivity. The possibility of two-proton emission from a nucleus which is stable against single-proton decay is a direct result of the binding energy of the even proton exceeding that a

b

e

Ep even

~p cold

Z=b2rnc 2k 2m+l l 2m

Z = 1 2 m 4 2 ' 2 m + l ' 2m

i

Fig

3 Two-proton

'

Z='2m+2'2m+l' 2m

'

radioactivity.

of the preceding odd proton, i.e., it is thus clear that the properties of a stable diproton within the nucleus should become apparent in two-proton radioactive decay. Moreover, the angular and energy distributions and correlations of the emitted protons are found to be dependent on the nature of pair interaction of the protons in the initial nuclei. On the other hand, since break-up of the diproton occurs in a "tunnel" through the barrier it determines the effective height of the barrier and its penetration. Thus, the simplest approach to the theory of two-proton decay would consist in using the product of two usual barrier factors, that is, in introducing an exponential factor of the type

w(E)

exp

{--

1 11

/12/

where Epp is the sum of the energies of the two protons (energy of emitted diproton), x and (1 - - x ) are the fractions of energy referring to each of the protons. It can easily be seen that the total barrier factor w(E) is maximum for x = 0.5, i.e., when the proton energies are equal. It will be noted that the value in the exponent is just the same as for the sub-barrier emission of a diproton with the energy Epp as a whole. Thus, the break-up of the sub-barrier diproton does not change the permeability of the barrier if no additional interaction (such as Coulomb repulsion) between two protons are considered. The probability w~(E) for such twoproton decay when the energy imparted to one of the protons is (0.5 --- ~)Epp

494

v i GOLDANqKY

(n -.~ 0.5) and that imparted to the other proton is (0 5 + N)Epp 1S related to [w(E)]__x = wo(E) by the relation

w~(E)

exp [

6~ (Z - - 2) e z ~/ M ~z }

Wo(e)

I

J

It is evident that the energy correlation between the two protons during t~oproton decay, which leads to their energies being almost equal, is quite strong. This correlation offers the possibility of detecting two-proton radioactivity even for almost immediate two-proton decays (by observing the equal;ty of energies for two sub-barrier protons). The interesting problem concerning twoproton radioactivity of neutron-deficient isotopes of even elements certainly deserves a more detailed special study.

6. Further Remarks It m a y be noted here that the most feasible way of obtaining neutron deficient isotopes of light nuclei is to bombard the lightest stable isotopes of neighbouring nuclei with protons or He 3 nuclei possessing energies close to the threshold value and also to use the heavy-ion nuclear reactions. However, one should keep in mind that owing to the low energy of the Coulomb barrier "boiling a w a y " of protons wili not be inhibited and hence the cross sections for production of neutron-deficient isotopes should be small. In conclusion we shall note that in the case of neutrons a phenomenon similar to two-proton radioactivity may occur. The excitation energy of nuclei with large neutron excess and even number of neutrons, at which the emission of neutrons becomes possible, may prove to be lower than the threshold foI the emission of one neutron owing to pairing effects. Therefore, for such nuclei there may be an excitation energy interval corresponding to the emission of neutron pairs correlated in angle and energy, without emission of single neutrons. Still more frequent must be the cases when the strongly excited states of neutron-saturated nuclei with an even number of neutrons m a y break up emitting one neutron as well as a correlated neutron pair. If similar excited states arise after a preceding fl-decay, they can be observed by the coincidencedelayed neutron pairs.

7. Conclusions i) The difference between the Z-th neutron and Z-th proton binding energies for any pair of mirror nuclei is determined by the formula

AE.p----En(NM~)--Ep(zMaN) ~E,(zN2z z ) - E p ( z M ~ z) ~ 1.2 which shows that it is independent of N.

Z--1

( 2 z - 1)~

MeV,

ON N E U T R O N - D E F I C I E N T ISOTOPES

495

2) With the aid of this formula it is possible to predict the existence of almost 90 new neutron-deficient isotopes of light nuclei (Z -- 8 - - 34) and also their properties (mass-defects, neutron and proton binding energy, fl-decay energy and half-period). The limits of stability of neutron-deficient isotopes of light nuclei against proton and two-proton decay are indicated. 3) Proton-radioactive decay and also the specific phenomenon of twoproton radioactivity can be observed near the indicated stability boundaries. 4) The main features of two-proton radioactivity are discussed. The author is sincerely thankful to Ya. B. Zeldovich for useful discussions. References 1) F A]zenberg-Selove and T Launtsen, Nuclear Physics 11 (1959) 1 2) V A Kravtsov, Uspekhl Flz Nauk 65 (1958) 451 3) A I Baz, Atomnaya Energla 6 (1959) 571 4) Ya B Zeldovlch, J E T P 38 (1960) 1123 5) V I Goldansky, J E T P 38 (1960) 1637 6) N Swamy and A. Green, Phys Rev. 112 (1958) 1719 7) B S Dzhelepov, Izvestlja Akad Nauk SSSR S e r - F l z IS (1951)498 8) G F Bogdanov, N A Vlasov, S. P Kahnln, B V Rybakov and V A Sldorov, A t o m n a y a Energia 3 (1957) 204, no 9