APPENDIX I

Alpha-Particle Half-Life Determination

The calculation of the lifetime of the alpha pa,rticles was ac- complished with the timing illustrated in the last two lines of figure 7.

One assumes, for this calculation. that the beam intensity is nearly constant throughout the measurement and that it strikes the target for the same length of time during each cycle. This implies that the activity of the target is the same at the beginning of each counting period, or that the number of cycles is sufficiently large to average out any effects due to va.rying target activities. If the number of N16

formed at time

t llt 0 is given by A .• then the number remaining after a time twill J

-t~ 16

be given by A. e where ~ is the decay rate for N • The number J

of decays counted in the fast 8caler after one cycle will be given by.

C A .(e -t1 \ -e

-t2~ +

C B

.(~ts

.. T)A -e

.(~-T)4

⁾

o J 0 J (30)

where B j represents the activity at t

*

T for the' second half of the

cycle, and Co is a constant

ot

proportionality depending on the geometry of the counter. The total number of counts in the fast scaler N

f ^is given by the sum of the above expression over all j cycles.

(31)

~63-

A similar expression results for the number of counts in the slow scaler N •

s

(32)

By making use of the a.bove assumption one can equate Aj to B j' and then the ratio, R. of counts in the fast scaler to counts in the slow scaler is given by.

N

_f

R c - :

N s

-t X

-t

~

-(t ...

T)A

1 2 5

e -e

+

e

-t ~ ... t A ... (t -T)A

3 4 7

e -e + •

-e (33)

The values of ti were obtain,ed by ating a 60 cycle pulser with the switching circuit. The following values resul.ted.

Table VIII ^t,

1

tl 1. 05 sec t -T

5 1.00 sec

t2 7.15 _{t6 -T} 7.20

t3

6.75

_{t -T}

7

6.92

t4 12.28 _tS·T 12.55

The above equation for R can be solved graphically by substituting different values of A and obtaining corresponding values for R. A curve can then be plotted of log R versus A which is nea.rly a straight Hne over the range of 0.0

<

A

<

0.4. The experimentally determined

- -

value of R is

-64-

Rzl.83+0.1Z.

From the graph of log R versus ~ one obtains a value for ).. which when converted to halloolife givee t ¹ == 7.3 + 0.7 seconds, which agrees

'2 -

well with the values quoted by (Blewer 1947) of tl =: 7.35 + 0.05 seconds.

2' -

and (Martin 1954) of 7.38

!.

0.05 seconds •.

-65 ..

APPENDIX II

Calculation of the Target Response Function

14 2,1 .

The range of N in Al has been measured by D. Powers (Powers 196Z) and is presented in the second column of Table IX. In

14 .58 order to convert these range measurements to the case of N in N1 equation 34 was used. Equation 34 is a.pplicable for M 1

<

M Z.

<R> a

av

and € is given by

0.68·

Z Z

MZ (z

3 +

^Z

"3)

^E

Z 1 Z 1

Z 1 Z Z (M 1

+

MZ)

(34)

(35)

By sUbstituting the proper value. into equations 34 and. 35. one obtains the range a.t a constant energy by the following relationship.

<R(Ni» c Z. 03

1

<R(Al»

At constant energy

The range was reduced by 6. Z% to transform the range for N 14 to th'e

16 .

range for N • The factor of 6. Zey. was also obtained from equations 34 and 35. The corrected ranges are given in the third column of Table IX.

Table IX

N

energy <R(A127

» <R(Ni5~1

Stragglin~

kev P:I' cm -2

e

S' cm ti' cm-

50 31

+

10 59 ⁴¹

100 75

+

8 142 25

200 116

+

13 Z21 4S

300 IS8

+

1" 300 61

400 201

+

15 381

46

SOO

221

+

17 419 58

When the N 16 nuclei recoil, their distribution will be symmetric about the beam axis and can be determined from the reaction dyna.mics and the above stated range-energy relationship. Let us define the dis- tance along the beam axis as the z direction and the origin of the

coordinate system will be the point of interaction.' p{z) then describes the distance of the N16

recoil from the beam axis. From the reaction dynamics one obtains the energy of the N 16 recoil for a given value of recoil angle

r..

^{and by} combining this energy with the range-energy relationship the position 01. the stopped N 16 can be obtained where:

p(z). <R> sin {. (36)

This determines a surface of revolution which contains all the N16

recoils. Of cour.e. one will obtain four different surfaces. one for each . of the different levels involved in the reaction. These four surfaces are

then averaged to give one common surface. This average was a weighted

-67-

average computed for constant z. and the values of p(z) were weighted according to the number of N 16 recoils present on each surface.

In order to perform this average one must know the density of N16

nuclei along each of the surfaces. N(e).· The (d. p) stripping reactions to the ground state and the first three excited states of Nl6

\

bave been studied by Zimmerman (Zimmerman 1968). The relationship used to convert from the center-of-mass system to the laboratory system is given in equation 37. where (J is the angle of the light particle in the

(37)

center-of-mass system. , is the angle of the heavy particle in the laboratory system. a.nd ^CT represents the respective cross-sections.

This is then converted to the density of particles along the beam direc- don.

N(z),

according to ectuation

S8:

N(z): 211 o{')

~

sin {. (38)

N(z) is presented in Table X for the four levels involved in the inter- action. The Bum of N(z) for the four levels is also presented. The va.lue. for the sum of the N 16 densities and the weighted average of

p(z) were used to determine the distribution of N¹⁶ nuclei at a constant depth L' cos w where L is the distance the a.lpha particle must travel in the target before escaping and being counted in the Bolid-state counter.

-68-

Table X. ^. N(z) for different levels in N ¹⁶

£(N16

) 0.00 0.119 0.295 0.392 2N{z)

. z(ttS· em ) -2 ^E

25 ⁰ 140 ⁽⁷⁾ (600) 747

SO

12

SO

18 300 380

75

^{28 7 50 65 150}

100 '2.7 7 62 IS ^{I I I}

150 23 18 42 37 120

ZOO 17 18 25 52 ^{11 Z}

250 13 14 IS 47

89

300 11 10 9 38 68

350 12 7 9 1.7 55

400 IS 3 ¹¹ 17 46

450 16 2 15 6 39

500 18 ( 0) ( 19) ( 0) 37

L ::I Z tan w

+

p(z) cos 'V (39)

'V is the angle that pta) makes with the scattering plane, such that when ^{"y •} 0·. p(z) lie. in the scattering plane and is directed away from the alpha-particle counter.

The density of N 16 on the surface of revolution, N(s), was determined by dividing N(z)ds by the area of a circular strip with radius p(z), equation 40. This surface density was then projected

N(s) •

~

~ ⁽⁴⁰⁾

onto the scattering plane where N(p) is the density in the plane. This density was integrated along the • variable for a constant value of L

N(p) :I Z N(e)

sin 'i (41)

wbere the constraint on z is given by equation 39. By using equation 39. p(z) lin '( can be replaced. and the integral over z becomes:

. N(L) N(z) dz

I (42)

Z 2 2

1f [p ..(L .. ^II tan w)

1

where N(L) is the linear denSity as a function of L, atld zl and z2 are given by the following expressions:

Z II

1 tanw

This integral was then evaluated using Weddle's six-point rule in order to obtain the densi ty of N16

nuclei as a function of the distance traversed in the target before reaching the solid-state counter. This dependence is given in Table Xl for a target angle w. IS-. The straggling was

taken into account by folding a gaussian function with a SO r'S' cm-2 width at balf-height into the calculated distribution. The distribution of N16

nuclei was converted to an energy loss spectrum for a monoenergetic alpha-particle source with E • 1. 65 Mev. The values of L were

(1

-70-

converted to alpha-partide energy lost. by assuming that the stopping power was nearly constant over the region of interest and was given by

em Z -kev

E • 0.82. • The resultant response function is shown in figure

iJ.g

12&.

Table XI

Lll:!:l-cm

-~

N~L~

0 2.76

10 2.56

ZO 2.63

30 2.52.

40 Z06

65 150

90 12.6

115

99

140 98

165 96

190 81

215 74

240 61

250 62.

Figure 1. 12 Energy levels of C

-71a-

11 12 .

The B (d. p) reaction produces B nuclet at an energy

E ^II/! 1.8 Mev with a cross-aection of 290 millibarns (Cook 1957a)

d

which then beta-decay to various excited states in C 12 as indicated in figure 1. The states of interest in thi s experiment are the 7.656 ..

Mev and 10. I-Mev states. Both of these states alpha-decay either by passing through Be8

~ it.

two body decay or by breaking up di- rectly in a three body decay. The energy spectrum of the alpha particles from these two states is illustrated in figure 3. The spec- trum varies from zero up to 1.8 Mev, and has been successfully described by Cook as a eerie. of two body decays.

-71-

Figure I

10.84 10.1 9.63

a

7.656

7.370

Figure Z. Charge exchange curves for He 4 When one observes reaction products through a magnetic analyzer, one must know what the charge-exchange fraction is in order to calculate the total yield. Figure Z shows this charge-exchange fraction. The insert in the upper right hand corner indicates the method used by O. Dissanaike (Dis- sanaike 1,953) to determine this fraction. He scattered a beam of alpha particles at 90· from metal foils of beryllium. aluminum. and silver. The scattered particles were then separated by a magnetic field. The charged particles were counted by a zinc sulphide screen .while the neutral particles were coUnted by a secondary-electron-multiplier. The beam was monitored using another secondary- electron-multiplier opposite the magnet and at 90· to the incident Mam. The quoted accuracies are

+ 1JI/.

for E

>

0.5 Mev and

+

510 for E

<

0.5 Mev; and the charge-exchange. fraction was asserted -e -e to be independent of the target material. The circled points were determined from the present experiment by assuming that the solid angle of the magnetic spectrometer was constant over the field settings of interest, and that the neu- trals (in the energy region where the neutral correction was important) were given accurately by the work of Dissanaike. The charge-exchange fraction can then be computed by comparing the number of singly ... charged alpha particles to the number of doubly-charged alpha particles at a given energy. The deviation of the circles from the curves indicates the magnitude of the discrepancy.

•

~ IV III I

• Dissanaike X Stier 1954

o

Experimental

Charge exchange for He4 1953 monitor EIOO 0 beam <l>

\

.J:J

X X - Xx

0

-

0

\ X - X XX. X / -

C

X

<l>

X Xx

u

X X X

X X X 201- X X

/

01 I X--XX!:::

I I

I :l ~ • • 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

4 Heenergy in Mev

... J (\)

"

10 C

....

(1) N

Figure 3. 12 Alpha-particle spectrum from C The reason for repeating the B 12(p)C

1~Be8 +

He 4 experiment was to obtain qualitative agreement with the results of C. Cook!!..!!. (Cook 1958). This agreement would indicate that the ex- perimental arrangements were functioning properly. Figure 3 compares Cook's data. points with those of the present experiment. The apparent disagreement around 1.3 Mev is probably due to the method of normaliza- tion and the fact that poorer resolution, points than was used previously by Cook.

~

• 121.. was used in obtaining the recent experimental p " A"

2.f •

510, (Cook 1957a). The curves were normalized to p the same height at a Bp setting of 300 kilogauss-em. The area. method of normalization was not used because of the difficulties involved in estimating the area under the solid-state counter curve. These difficulties arise from the uncertainty in the beta-particle background. The background can be seen clearly on the drawing. The agreement was considered adequate to justify not repeating the quantitative pal"'t of the BIZ experiment and to indicate that the experimental arrangements were suf- fiCiently sen.itive to detect alpha-particle decay from the N16(p}016 etc. and FZO(p)NeZO etc. ro- actions.

t -..l ~ I»

•

(/)

-

C ::J ~ L- o L-

-

..0 L- o c

1000

800

608 a. 400 1:J

-

a. Z 200 Alpha-particle energy in Mev 0.025 0.1 0.25 0.5 1.0 2.0

:\ ,

\\ bet a -par t i cl e backgrou nd

~o r ~o

\ \

~xo

0 \ \

~

__

O~ \ >b

~ o Cook's experimental points

(57~

, -Theoretical yield (Cook 1958) ;

~ o

Sol i d -s tat e co un t err e sui t s (60)1

O~

0 x Magnet analysis (59) \ '"

, <Y

3.0

I -..J ()J "TI 10 C ~ CI) I '), ! > 'r DIe r=:: OJ 100 200

300 400

500 Bp in kilogauss-em

Figure 4. Energy levels of 0 16

-74a-

N16

beta-decays from its ground state to various levels in

o

16 ^with the branching ratios indicated 1n figure 4. The excited

levels of interest are the 9. 85.Mev (z+) level. the 9. 59-Mev (1-) level and the 8. S8.Mev (Z .. ) level. The first two are allowed to alpha-decay to ClZ

while the last is not. Heretolore the first two levels were not known to be populated by the beta-decay process. Alpha particles from the

9.

59-Mev level were observed. figure Zl, with a peak energy of 1. 69 Mev in the laboratory system. The shift 1n energy of the spectrum's peak from the value obtained from the reaction

dynamics was consistent with the theoretical shift induced by pene- tration factors, beta-decay phase-space, target geometry, and

solid-state counter effects as discussed 1n sections ID-I and IV -A. B.

The 8.88-Mev level is forbidden by spin and parity to emit alpha particles. The absenee of alpha particles from this level givee rise to a limit on the positive-parity admixture in the 8. SS-Mev level.

and thus a limit on the magnitude of the parity non-conserving term in the nuclear potential.

7.162 0+

e

^l2

^+He

⁴

10.36 9.85

9.59 8.88

7.12 6.92 6.13

-74-

6.05 0+

Figure 4

±

0.2). 10-⁵

10.683

...,.--""":"'-'.L..J..:L..:=..2 - N'

⁵

+ d - P

Figure 5. Experimental arrangement A deuteron beam from the Kellogg Z-Mev electrostatic accelerator is incident on a mass separating system and then magnetically analyzec1. A tantalum shutter above the analyzer inter- rupts the beam according to the timing schedule illustra.ted in figure 7. After magnetic analysis. the beam enters the target chamber and strikes the target at a target angle. w. lS-. where w is defined in figure 11. For a detailed discussion of the target chamber see figure 6. The reaction products are analyzed at a labQratory. angle, ~ • 90·. figure lZb. by either a solid-state counter or the alternating gradient magnetic spectrometer (Martin 1956. 1957). The gamma rays were mon- itored in a plastic scintillator (1.70 inches in diameter and 0.62 inches deep)or a NaI crystal (Z. 0 inches in diameter and Z.O inches deep) oriented in the hori:r.ontal plane at 48-to the incident deuteron beam. In addition to the lucite target chamber walls. a 1. 5-inch-thick carbon absorber was placed between the crystal and the target chamber to absorb the beta particles.

I -J \J1 ?> I

~ Deutron beam from 2-Mev accelerator separator magnet .. Moss separator collector slits Joo.-Beam shutter .---Du m 0 n t 6292 Magnetic analyzer To biased scaler To 100 channel analyzer ... '\.

-

Orthogonal slit system

II 4+---I I II To 10 or 100 ~ channel analyzer

~--Pb shield .----NaI scintillator .----C absorber counter shutler Alternating gradient magnetic spectrometer Dumont 6291 or

I -..,J (Jl solid-state counter " 1.0 C

"'"

(t) (Jl

Figure 6. Target chamber This figure illustrates the geometrical arrangement of the counters and the target chamber shielding system. The solid-state counter is mounted on the left and is sealed in the vacuum system. The counter solid angle can be adjusted by varying the two positioning screws shown above and below the counter. The counter is mounted behind a O.OlO-inch-thick tantalum shield with a 3/16-inch- diameter bole in its center. The area of this hole and its distance from the target deCine the solid angle of the counter. A O.0064-mm. aluminum foil mounted over a ~/8-inch-diameter hole in a tantalum blank is suspended from a single pOint such that it rotate. u.nder the force of gravity when the counter mount is rotated about its axis of symmetry. This foil was positioned over the solid-state counter in order to absorb the alpha particles while the background was being determined. The target shield, a O.OZO-inch-thick right circular cylinder of tantalum one inch in diam- eter with a 3/8-inch section removed for the beam, is shown in the "beam ontl position. The beam strikes the target activating the N15 • and the recoiling N16 and scattered deuterons that escape from the target are collected on the tantalum shield. Wben the beam is turned off the shield drops and the fiat tantalum plate covers the entrance aperture of the target chamber. This plate intercepts any residual beam that may pass down the beam tube during the counting part of the cycle. Typical spectrometer parameters for these experiments were

~ -1210

and

.fl..

0.01 ster. p

« -.I 0" III

•

Targ etch ambe r and count er are presented in a simple cut-away view. Solenoid, target and To shield are presented in perspective, as viewed from slightly above the beam axis in the direction of the incident beam. AI foil on Ta frame ;

Top r 0 tr act 0 ran d cur r e n tin t e g rat 0 r

..

I I I I 1 I 1"'1-...

/-,

') .... )

: €II

~;O I i i Beam spot To shield To vacuum system Ta shield is in the beam on position. Magnet entrance aperture

I

""'"

en

.,

1.0 C ~ CD CJ)

I

Figure 7. Timing Before the start of a given cycle the scalers are gated off and the alpha-counter bias is turned off. The cycle is started by turning on the spray supply for the belt. The accelerating volt- age increases gradually and the accelerator requires about three seconds to reach the final energy after which the beam strikes the target for about eight seconds before the spray supply is tu.rned off. The voltage on the accelerator decays with a time constant of five seconds. In order to stop higher mass beams from striking the target as the accelerating voltage decreases, two shutters intercept the beam. One is above the.magnetic analyzer (figure 5) and the other is in the target chamber (figure 6). The bias on the solid-state counter is applied immediately after the beam leaves the target so that accumulated charges can be swept out of the barrier region befOTe the gates to the scalers are opened. 1.5 seconds later. Switching pulses do not affect the scalers because the scalers are gated off during the switching periods.

I ..,J ..,J I»

•

a b c d a

Spray supply for on electrostat ic acc. off

--1

11.3 13.7 11.2 13.7

I

y-electronics gate

l

13.7 11.1 13.7 11.3 a-electronics gate

L

14.0 11.0 14.0 10.9 a -counter voltage Scaler gates for lifetime ve r

if

i co t ion

I

11.4 13.4 11.6 13.4

L

tl t2 t5 t6 "fast" 19.1 I I 6.1 I 19.1 I I 6.2 ... 1 __ _

t=Q t=T

t3 t4 t7 ta II II 'I

I

slow I 19.2 5.5 19.2 5.6 L....-_ ~5sec ~ time ;;..

." 10 c: .... (1) ...

---.J ---.J

Figure 8. Target thickness The target was made and its thickness was measured by D. Hebbard (Hebbard 1960). By using the N15 (p,Cl"1)C .2 reaction and studying the gamma-ray yield as a function of inc;ident proton energy. one can obtain the distribution of N15 in the target. The resonance used occurs at a proton energy of 0.4Z9 Mev and has a width.

r •

800 eVe The target was 7 key thick to 0.431- Mev protons which corresponds to 28 key for 1. 7-Mev alpha particles (Whaling 1958). This represents a surface density of 1.8.1017 target nuclei. em -Z.

• ..., f •

"'0

-

Q) >- >- 0 ~ I

/- ~

0 E E 0 0'1 Q) >

,e -

0 Q)

a:: 425 430 435

...

Thickness of Ti N

I5

target to 431-kev protons N

I5

(p, a y) 440 445 450 455 Proton energy in kev

460

""Tl ID C ~ ro CD

I -,J (JJ

Figure

9.

Solid-state counter calibration A typical calibration curve for the solid-state counter is shown in figure

9.

The data points were obtained by three different methods. The crosses were obtained by scattering alpha particles from a thick gold target through the alternating gradient spectrometer into the counter. The open circles at 1. 75 Mev came from scattering the alpha. particles througb a thin gold foil directly into the solid-state counter. The solid points at Z.65 Mev came from a poZlO(E

=

5.3 Mev) Q source after the arnplifer gain had been decreased by a factor of two. The scatter in the last two groups was due to gain changes in the amplifier, and indicates the order of magnitude of the cor- rection to the abscissa that was ne(:essary in order to combine the spectra of different days.

t -J -D PJ

•

'-Q)

-

^C

::J o

U

-

Q) ^o

-

^(J') _I

\ j

o

(J')

'-o

-.-

Q)

>

'- ::J U C o

-

^o _'-

.0

o

U

-79-

\ _x

\ ^x

9

\ x

a a

a en

(X)

a

a

t-- '-

Q)

..0

E

::J

a

^C

lD

Q) C C

o

a u

,£;

10

a

'\t

a

r0

.. aOa-

Figure 10. Monitor gamma-ray spectrum

This flgure displays the gamma-ray spectrum whicb was uBed to determine the total number of beta-decays that occurred during the counting period. The branching ratio of the beta-decay to the 7.1Z .. Mev and 6.13-Mev levela in 016

was given by Ajzenberg- Selov. and Lauritsen (Ajzenberg-5elove 1(59). and thus by working backwards one can obtain the N16

activity during the counting cycle.

The bias of the monitor scaler is shown on the drawing. The gamma rays were counted in a cylindrical Z x Z inch Nal crystal that had a 1.5.ineh.thick carbon absorber interposed between the source and the crystal in order to stop the beta particles. The efficiency of

. . 19 16 .

the monitor counter was determined using the F (p. a. -V)O reaction with the same geometry that was used in the

N16(f3)Ol6~

^{ell ..} He 4

ex~riment. The measured efficiency was O~ Z4%. See section Ill-H.

-

(/) ^c _~

o

U I

>--.

1,000

500

100

50

-80-

Figure 10

y-ray pulse height spectrum from OIS*_ y+OIS

Monitor scaler counted pulses above channel 44

7.1

1 ,

10~----~~~~~----J---~---~----~----~

40 50 60 70 80 90

Channel number

Figure li. Geometric effects As the target angle fa.) is decreased from fa.):11 48-to CIa • 0-, the number of recoil N16 nuclei that escape from the target surface increases from none to one half of the induced activity. See sec- tion UI.I 0 The N16 nuclei that escape from the surface during bombardment are caught on the tan- talum shield and are removed from the field of view of the solid-state counter when the shield drops. If the gamma rays following the Nl6 decays on the tantalum shield were observed in the monitor scaler, the 0./"1 ratio would decrease as" the target angle is

decrease.d~

and the number of escaping N16

~uclei

increases. Results of the measurem~nts of the angular dependence of this ratio in figure 11a show that it is constant to within the experimental accuracy. The variation of the solid angle is 11-between w.lS- and w • 45· and has been neglected. As the target angle is decreased the absolute number of N16 produced increases as cosec CIt "because the effective target thickness increases as the cosec w. If this factor of the angular depend- ence of the number

of

Nl6 created is factored out of the observed gamma-ray yield, the resultant yield should decrease with target angle iIi proportion to the number of recoil N16 nuclei that escape from the target surface. This is illustrated in figure Ub. where the normalization is such that 1001. of the N16 formed are counted at ~ • 48°.

•

OG

....

I»

•