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Measurement of the off-resonance cross section of the 6.4 MeV 1H(15N, αγ)12C nuclear reaction
1
Nuclear Instruments and Methods in Physics Research B34 (1988) 1-8 North-Holland, Amsterdam
MEASUREMENT OF THE OFF-RESONANCE CROSS SECTION OF THE 6.4 MeV ‘H(15N, c~y)‘~C NUCLEAR REACTION * KM. HORN and W.A. LANFORD
Received 4 January 1988
Measurements of off-resonance yield from the 6.4 MeV *H(15N, ay)“‘C nuclear reaction indicate that the off-resonance cross section is 77 pb, much smaller than the currently published value. A procedure for directly evaluating the off-resonance gamma-ray yield detected during hydrogen profiling measurementsis presented. The absolute on-resonance and off-resonance cross sections of this nuclear reaction are evaluated.
1. Intruduction Since the inception of the use of the 6.4 MeV rH(15N, ay)“C nuclear reaction as a tool for profiling hydrogen concentrations within solid targets [I], the cont~bution of yield from off-resonance reactions has been a concern. However, corrections to measured yields based on the published value of the off-resonance cross section [Z] have not agreed well with experimental data, often predicting yields in excess of those actually measured. Because of the difficulty in preparing a suitable hydrogen target for precise measurement of the off-resonance cross section (i.e. a thin, stable, hydrogen-rich surface layer covering a hydrogen-free backing), the cross section has ~sto~e~ly been determined using a thin r5N target and a proton beam. However, recent hydrogen profiling measurements we have made in hydrogen gas environments have highlighted the inaccuracy of the currently accepted value for the off-resonance cross section and prompted a more careful examination of it. In utilizing the rH(r5N, ~uy)‘~C nuclear reaction for detecting hydrogen, the target is bombarded with a beam of r5N ions at energies of 6.4 MeV and above. At 6.4 MeV (the reaction’s resonance energy) a reaction can occur between an incident nitrogen ion and a target hydrogen nucleus producing a characteristic gamma-ray of energy 4.43 MeV. A -g~a~ray detector is used to measure the yield of these characteristic gamma-rays. For a given number of incident r5N ions, this yield is directly proportional to the amount of hydrogen in the target at the depth at which the beam is at the resonance energy. When the energy of the incident r5N
(a)
I-
HYDROGEN-BEARING
LAYER
(b)
Fig. 1. Schematic representation of the (a) on-resonance and (b) off-resonance condition.
* Supported in part by a grant from IBM Corporation. ~~68-583X/88/$03.50 @ Elsevier Science ~blishers (North-Holland Physics Publishing Division}
beam is set to the resonance energy of 6.4 MeV, the measured gamma-ray yield results from reactions with hydrogen on the surface - see fig. la. At higher beam energies, the incident ions do not reach the resonance energy until they have penetrated some distance into the target, owing to stopping power effects. Therefore, as the beam energy is increased, the resonance probes successively deeper regions of the sample resulting in a profile of the hydrogen con~ntration in the target as a function of depth. When the resonance is deep within the target, a hydrogen-rich surface layer can interact with the incident beam of nitrogen ions through the off-resonance cross section - see fig. lb. Though this cross section is many orders of magnitude less than the on-resonance cross section, the gamma-ray yield from the interaction of a hydrogen-rich surface layer with the off-resonance cross section can rival or surpass the yield arising from the resonance cross section probing a region ~ntai~g little or no hydrogen‘
B.V.
2
KM. Horn, W.A. Lanford / Off-resonance cross section of the 6.4 MeV ‘H(‘%
Evidence of the inaccuracy of the currently accepted off-resonance cross section of 500 fib [2] became apparent during measurements of the hydrogen concentrations present at the interfaces of m~~ayered samples while these samples were in a 1 Torr hydrogen atmosphere (33. Contrary to expectations based on a cross section of 500 pb, we found that even in the presence of a huge hydrogen surface signal (corresponding to the 1 Torr of hydrogen gas surrounding the target) it was possible to probe thousands of ~ngs~~~ into a clean, untreated, single crystal of silicon with surprisingly high sensitivity. Nevertheless, a small, yet constant, extranwus gamma-ray yield was observed whenever targets were measured in a 1 Torr hydrogen atmosphere. ?Vhen the effect proved to be dependent only upon the hydrogen pressure in the gas cell, it became apparent that the additional yield was the result of an interaction of the gas-phase hydrogen with the off-resonance cross section. Though the effects of the off-resonance yield were clear, the unwieldy geometry of our gas cell precluded the precise determination of the off-resonance cross section using a gas-phase hydrogen target.
c~y)‘~C reaction
_-
II IC3
SC0
JOC
CHANNEL NUMBER
2. Experimental In order to gain the high statistical accuracy needed to arrive at au accurate value for the ‘H(15N, ory)i2C off-resonance cross section, we required a target with a large hydrogen concentration confined to a relatively thin layer of a few thousand tigstriims. The target also had to be stable under prolonged beam exposure (i.e. hundreds of nA over several hours}. Previous work done by Lanford and Guo [4] indicated that thin titanium films can be hydrated to a stoichiometry of approximately TiHa. Being both rich in hydrogen and stable under long ion beam exposures, titanium diiydride is an excellent target for this cross section measurement. The tit~ium dihydride target was made by evaporating pure titanium onto a clean silicon substrate at 10e6 Torr vacuum in a diffusion-pumped evaporation chamber equipped with resistive-hits evaporant boats. After the evaporation, the sample was annealed in a hydrogen atmosphere at 350 ’ C for 30 min. Once hydrogenated, the hydrogen content of the sample proved to be stable over many months and repeated exposures to the ion beam. Presented in fig. 2 is a c~~acte~~tion of the TiH,/Si(lOO) target used in determining the off-resonance yield correction. Fig. 2a is a Rutherford backscattering spectrum of the target showing it to be composed of a titanium layer with an underlying silicon substrate. Because Rutherford backscattering is iusensitive to elements of mass less than or equal to that of the incident projectile (helium ions, in this case) the hydrogen present in the sample is not detected. Fig. 2b is a hydrogen profile of this same target using the
fc)
BEAflENERGY
[Me'4
Fig. 2. Analysis of the TiH,/Si(lOO) target using (a) Rutherford backscattering and (b) hydrogen profiling. An expanded view of the off-resonance region is given in (c).
*H(“N, ~uy)“C nuclear reaction technique. Between the energies of 6.4 MeV and 7.05 MeV, the large hydrogen content of the titanium dihydride layer in the target is apparent. In profiling the off-resonance region from 7.25 to 8.0 MeV, the number of incident nitrogen ions per data point was increased by a factor of ten over that used to profile the hydrogen-rich titanium layer in order to increase the accuracy of the off-resonance yield measurement. Fig. 2e is an expanded depiction of this off-resonance region of the hydrogen profile shown in fig. 2b.
K.M. Horn, W.A. Lunford / Off-resonance cross section
ofthe 6.4
MeV ‘H(“N,
oiy)“C reaction
3
section might, in fact, arise from the interaction of the resonance with hydrogen deep in the bulk. Therefore, for comparative purposes, Fig. 3 displays the results when the same characterization techniques are applied to the back side of the silicon substrate which was protected from the titanium evaporation, but fully exposed during the hydrogen annealing. As is clear from fig. 3b, the only appreciable yield detected when profiling the back side of the silicon substrate is on the surface, the result of contamination from the ambient hydrocarbons in the vacuum of the analysis chamber. Within the silicon substrate essentially zero hydrogen is detected.
3. Correcting for off-resonance files
B-0
6.2
6.4
6.6
1.8
7.0
SEAM ENEAGY
72
7.4
7.8
7.8
D&VI
Correcting for off-resonance yield becomes a concern when measuring low concentrations of hydrogen in the interior of samples with overlaying layers which contain significant amounts of hydrogen. Such correction, however, is easily accomplished in the region in which the off-resonance cross section remains fairly constant (up to 8 MeV), by simply subtracting from the measured gamma-ray yield a number of counts proportional to the amount of hydrogen subject to the off-resonance cross section. This proportionality constant can be determined from the data of fig. 2b. Here, the area under the hydrogen bearing region of the hydrogen profile is 9.96 x lo6 keV . counts; the resulting average off-resonance yield is 127 (having corrected for the ten-fold increase in a~umulat~ charge with which the off-resonance data were taken). The number of counts arising from off-resonance yield when profiling past a hydrogen bearing layer, with integrated area I (expressed in keV . counts), is then simply: YOff-tes= (1.28 x 10-5)1.
BEAM ENERGY
[MeV]
Fig. 3. Analysis of the Si(100) side of the target using (a) Rutherford backscattering and (b) hydrogen profiling. An expanded view of the off-resonance region is given in (c).
It should be noted that the hydrogen profile measurements do not explicitly rely on measurements of the ‘H(“N, ory)“C reaction cross section. Rather, this hydrogen profiling technique was “calibrated” by measurements done on a variety of targets of known hydrogen content, including ion implanted samples [5]. In order to arrive at an accurate off-resonance yield correction, it is important that the amount of hydrogen in the substrate be zero or near-zero. Otherwise, the yield which we wish to ascribe to the interaction of the surface hydrogen layer with the off-resonance cross
yield in hydrogen pro-
(1)
The above correction formula was dete~n~ from measurements in which a 3 x 3 in. bismuth germanate (BGO) gamma-ray detector was positioned at 0 o to the incident ion beam and separated from the target by 2.5 cm. For other geometries, the correction constant derived from the ratio of the on-resonance to off-resonance yield must be adjusted to compensate for the differences in the angular dependence of gamma-ray emission of the on-resonance and off-resonance reactions. To illustrate this point, it can be seen from the angular distribution of gamma-rays presented in fig. 4 that the ratio of the on-resonance to off-resonance yield measured at 0” is more than twice as large as that measured at a beam-detector angle of 45 O. Though knowledge of the precise value of the on-resonance and off-resonance cross sections of the ‘H(r’N, cyy)“C nuclear reaction is not necessary in
K.M. Horn, WA. Lanford / Off-resonance cross section of the 6.4 MeV ‘H(-“N, cuy)12C reaction
the *‘N(p, cuy)*‘C resonant reaction and determined the probability of emission of a gamma-ray at an angle B to the incident proton beam to be, Bq 0) = [: + :cos2e - $cos‘q +&[1-3
n.31
OFF-RESONANCE 0 = 40 iJc i 1 i ,=-R-.-.-.-I-.-D-.-.--8 i
0
50
100
BEAM - DETECTOR ANGLE
150
[degrees]
Fig. 4. Comparison of the angular distribution of gamma-rays emitted by the 6.4 MeV ‘H(15N, ay)12C on-resonance and off-resonance nuclear reactions.
order to estimate and correct for the effects of off-resonance yield in hydrogen profiling measurements, the
TiH, target created for this experiment lends itself nicely to such a determination. Furthermore, the long history of measurements of the cross section of this nuclear reaction and revisions to its accepted FWHM make its re-examination desirable. To this end, on-resonance and”off-resonance gamma-ray yields were measured from a second, somewhat thinner TiH, target mounted in an experiment chamber which allowed precise measurement of the various parameters necessary to determine the reaction’s absolute cross sections.
cos2e + 4 co&q,
(2)
where x = 0.82 for the 429 keV resonance. In the ensuing years, the 429 keV resonance was m-examined in several works [lo-131 with no revisions of the accepted cross section or FWHM reported. In 1974, Rolfs and Rodney [2] presented a comprehensive examination of both the 15N(p, y)r6 0 and 15N(p, cyy)12C nuclear reaction cross sections. In this work, which showed that the 15N(p, cyy)r2C nuclear reaction makes only a negligible contribution to hydrogen burning at stellar energies, an above-resonance off-resonance cross section of approximately 500 pb (fig. 7a) was reported. With the application of the inverse 6.4 MeV ‘H(15N, ay)12C reaction to the measurement of hydrogen in solids in the mid-1970’s [l], it became apparent that the FWHM of the resonance was narrower than the 13.5 keV cited in the literature. A succession of lower values for the FWHM of the resonance were reported by several authors from 1976 to 1980 [14,15]. In 1983, Maurel and Amsel 1161 and Damjantschitsch, et al. [17] independently measured the FWHM of the resonance to be 1.8 keV. Taking the product of the historically accepted cross section (300 mb) and FWHM (13.5 keV) to be invariant, this new measurement of a FWHM of 1.8 keV implies a total on-resonance cross section of 1.6 b.
5. Determination of the 6.4 MeV ‘H(15N, aty)“C cross section
4. Previous measurements
of the ‘H15N, cuy)“C cross
section
Study of this nuclear reaction’s cross section began in the late 1930s as a part of the investigation of the carbon-nitrogen-oxygen cycle of stellar energy generation proposed by Bethe [6]. Fowler and Lauritsen [7] performed the earliest measurements of the 15N(p, (uy)12C reaction in 1940 by bombarding an enriched 15N target with protons; they reported the presence of resonant reactions at 0.88, 1.03 and 1.20 MeV. A more detailed investigation of the reaction by Schardt, Fowler, and Lauritsen [S] in 1952 detected a resonance at 429 keV with a measured on-resonance cross section of 300 mb and a full width at half maximum (FWHM) of 0.9 keV. For the inverse 6.4 MeV ‘H(15N, q)i2C reaction, in which a beam of “N ions is incident on a hydrogen-bearing target, the corresponding FWHM is 13.5 keV. The following year, Kraus, et al. [9] measured the angular distribution of gamma-rays resulting from
The total yield from a nuclear reaction experiment is given in its most general form as, Y=Nin,a(E)~,
(3)
where Ni is the number of incident ions, n, is the area1 density of the nuclei in the target, a(E) is the reaction’s total cross section, and e is the source intrinsic efficiency of the detector. The yield measured in a solid angle, Ati, at a specified angle, 8, to the incident beam is simply, Y(E,
8) = Nin,
do(E,
B)rAS2,
(4)
where do(E, 19) is the differential cross section of the reaction at energy E and angle 0 and the term eA0 is the incident intrinsic efficiency of the detector. The number of incident ions, Ni, can be expressed as the total amount of charge incident on the target divided by the charge of each individual incident ion, Q/q. For a target of arbitrary hydrogen content versus depth, the yield can be thought of as arising from a series of thin
5
K.M. Horn, W.A. Lanford / Off-resonancecrosssectionof the 4.4 MeV ‘H(“N, ay)12C reaction target slabs each of uniform hydrogen content, p(x). The total yield measured over a solid angle AP at an angle 0 to the incident beam can then be expressed more explicitly as the yield arising from each slab of thickness dx, summed over the entire thickness of the target, t. Y(E,
dx] du(E,
@)=jd[$][p(x)
B)EAL?.
5.1. Off-resonance cross section In applying eq. (5) to the off-resonance condition, it can be recognized that the differential cross section, d u( E, 8), is essentially constant over the energy range of 6.5-8.0 MeV and can thus be factored out of the integral. 8) = $A0
da(E,
B)ldp(x)
dx.
(6)
For a target of uniform or slowly varying hydrogen concentration, pH is a constant which can likewise be factored out of the integrand, the yield equation simplifing to: Y(E,
0) = +AP
da(E,
@pt.
2 >
.
.
500
ti
.
.
.
i
i
(5)
As has been shown in the literature, the on-resonance cross section of the 6.4 MeV ‘H(15N, cyy)“C nuclear reaction is sharply peaked about its resonance energy, possessing a Lorentzian-shaped excitation curve as described by the Breit-Wigner dispersion formula [18]. On the other hand, the off-resonance cross section averaged over the target thickness is relatively constant upto energies of 8.0 MeV, as can be seen from fig. 2c. Furthermore, the angular distribution of gamma-rays resulting from the on-resonance reaction, depicted in fig. 4, is distinctly different from that of the off-resonance reaction which exhibits only the weakest of angular dependency. Because of the differing natures of the on-resonance and off-resonance cross sections, the yield equation for each must be derived separately.
Y(E,
5loooi
(7)
In evaluating the off-resonance cross section, gamma-ray yields were measured from a 1800 A titanium dihydride layer using a 3 X 3 in. BGO detector, positioned three inches from the sample. These measurements were made at various angles relative to the incident ion beam, ranging from 0 o to 90 o in 15 o steps (see fig. 5). In this geometry, the detector’s incident intrinsic efficiency, eAO, is 0.241 [193 for the combined full energy and single escape peaks; the areal density of hydrogen in the TiH, layer, pHt was determined to be 1.92 x lOIs H/cm* through application of an empirical formula determined from measurement of hydrogen standards [5]. A total integrated charge, Q, of 80 PC was collected for each data point using a doubly ionized “N beam
BEAM - DETECTOR
ANGLE
[degrees]
Fig. 5. Measurement of the off-resonance gamma-ray yield from the 6.4 MeV ‘H(i5N, cyy)12C nuclear reaction. Target-detector distance is 3 in., integrated charge is 80 pC.
(therefore, q = 3.204 x lo-l9 C). Utilizing the off-resonance yield measurements presented in fig. 5, the differential cross section at 0 o is calculated to be 4.76 pb. Dividing this value by the solid angle subtended by the detector, 0.212a, the differential cross section per steradian at 0’ is 7.15 pb/sr. After calculating these values for each of the other data points, the total cross section, u, is determined by integrating the differential cross section per steradian over all angles [20]: U=
257
/.i0
sdu(Ey 0)
sb
0
de
dq
dG
0
Assuming no azimuthal dependence of the reaction’s gamma-ray emission, the integral over cp evaluates to 2a. The integral over 0 is evaluated numerically using modified, composite Simpson rule [21] over the range 0 = 0 to 7r/2. The gamma-ray yield measurements made at beam-detector angles varying from 0 o to 150 o (fig. 4) show no indication of any asymmetry about r/2 so, the result of the integration over this region is simply doubled to evaluate the limits 0 to a. The total off-resonance cross section at 7.4 MeV is calculated to be 77 pb. The result at this energy and several other energies is presented in fig. 7b. 5.2. On-resonance cross section Beginning again from the general yield expression of eq. (5), those variables that are kept constant during the experiment can be factored out of the integral leaving, Y(E,
0) = +APJoidu(E;
B)p(x)
dx.
(9)
The integral, which is initially over target thickness x, is converted to one over energy through the change of variable, dE dx = dE/dx
’
K.M. Horn, WA. Lmjord / Off-resonance cross section of the 4.4 MeV ‘H(“N, cuy)12Creaction
6
For a sufficiently thick target (i.e. one from which the ion beam does not exit) the energy of the “N ions within the target range from E = E,, the energy of the ion beam at the surface, to E = 0, after the ions have come to rest within the target. The yield equation then takes the form,
For a hydrogen distribution which is constant or slowly varying within the target, p,(E) can be taken to be constant over the energy range of this narrow resonance. The stopping power, dE/dx, which is also a function of energy, is likewise treated as constant over the energy range of the narrow resonance. Since the ions’ energy decreases with increasing depth, dE/dx is negative. In order that we may treat dE/dx as a positive value, the implicit negative sign will be absorbed into the integral by reversing the limits of integration. Extracting the constant terms from the integrand results in the yield equation:
Y(E, f3)=$rAPp c&&~Bdo(E,
@>dE.
(11)
The form of the resonant cross section given by the single level Breit-Wigner dispersion formula is [X3], da(E,B)
P/4
=da(E,, 0)
(12) (E-Er)'+T2,'4'
Substituting this expression into eq. (11) gives, Y(E,
e) =
$rA9p
X
EB
J0
n&d+&,
0)
r2/4
dE
’
(E-E,)2+T2/4
(13)
where do(E,, 0), the differential cross section of the reaction at the resonance energy of 6.4 MeV, is a constant that has been brought outside the integral. Evaluation of the integral results in a yield equation of the form,
Y(E, 0) = $AQ
du(E,,
e)P,&--;
O-
In the thick target approximation it is assumed that the resonance reaction occurs deep within the target; the beam energy, therefore, is taken to be very large, i.e. E, = co.For this narrow resonance, r/2 < EB - Er and r/2 << E,, so to a very good approximation, tan-‘( EB-Er)/(T/2)=a/2 and tan-‘(E,)/(T/2) = -CT/~.Eq. (14) then simplifies to:
60
BEAM - DETECTOR ANGLE
90 [degrees]
Fig. 6. Measurement of the on-resonance gamma-ray yield from the 6.4 MeV rH(“N, cuy)r’C nuclear reaction. Target-detector distance is 5 in., integrated charge is 4 pC.
In order to use this expression to determine the differential cross section, and ultimately the total cross section, gamma-ray yields were measured on the TiH, target with the BGO detector mounted five inches from the sample over a range of beam-detector angles ranging from 0 o to 90° (see fig. 6). Because the on-resonance yield from this reaction is so large, the detector was positioned further from the target than in the off-resonance measurement to better resolve the angular dependence of the emitted gamma-rays. As is apparent from the functional form of the angular distribution of emitted gamma-rays developed by Kraus, and as suggested by the measurements presented in fig. 4, the angular distribution of gamma-rays is an even function and therefore is symmetric about r/2, thus alleviating the need to measure beyond 90 o _ Each data point was measured with a collected charge of 4 PC, using a doubly ionized 15N beam. The detector’s incident intrinsic efficiency,
-tad+ 1. (14) -E
30
K.M. Horn, W.A. Lanford / Off-resonance cross section of the 6.4 MeV ‘H(“N,
ay)“C
reaction
7
6. Discussion The motivation for the present experiment was to obtain an accurate procedure for determining the number of counts observed in a hydrogen profiling measurement that are due to off-resonance reactions. Eq. (1) gives this contribution to the count rate for a 3 X 3 in. BGO detector mounted at 0 o to the incident ion beam. We believe that over our energy range (6.4-8.0 MeV) this expression is accurate to 15% or better. Since this contribution is so small, in most cases, this is more than accurate enough for hydrogen profiling purposes. The on-resonance cross section measurement m”ade in this work agrees quite well with the historically derived value, On the other hand, the off-resonance cross section of 77 gb measured in this experiment differs greatly from the literature value of 500 pb [2]. While it is difficult to know for certain why past measurement of this cross section resulted in such a large value, it is possible that this was due to a low energy tail in the proton beam. It is well known that unless great care is taken (polishing slits, antiscattering slits, etc.) proton beams can exhibit low energy tails with intensities of order lop3 to 10e4 of the total beam intensity. In the presence of such low energy tails, yield from low energy ions interacting on-resonance with the 15N target would simulate the off-resonance reaction. In contrast, N15 ion beams, because of their large stopping power, have very small low energy tails.
15NBEAM ENERGY jMeV1
j5NBEAM ENERGY [MeVl
Fig. 7. Total cross section of the 6.4 MeV resonance of the rH(15N, cyy)“C nuclear reaction (a) 1974 and (b) 1988. The resonance width of 1.8 keV depicted in (b) reflects the values
measured by Maurel and Amsel [16] and Damjantschitsch et al. [17].
computer program for calculating gamma-ray detector efficiencies.
References
PI W.A. Lanford, H.P. Trautvetter, J. Ziegler, and J. Keller, Appl. Phys. Lett. 28 (1976) 566.
7. Conclusion As is contrasted in fig. 7, over the past five years, the measured value of the cross section of the 6.4 MeV ‘H(15N, ocy)i2C nuclear reaction has changed dramatically. Maurel and Amsel[16] as well as Damjantschitsch et al. [17], in 1983 measured the FWHM of this resonance to be 1.8 keV, implying an on-resonance cross section of 1.6 b. In this work we have explicitly measured this cross section to be 1.56 b. The off-resonance cross section measurement of 77 pb is much less than the literature value of 500 p’b. The ratio of the on-resonance to off-resonance cross section is then 20800 - almost seven times greater than the most recent estimate [17]. As shown in fig. 7b, the cross section of the 6.4 MeV lH(r’N, ay)“C resonance changes over four orders of magnitude from on-resonance to off-resonance on either side, with a full width at half maximum of only 1.8 keV, making this one of the most aesthetically pleasing resonances in nature - or as G. Amsel has proclaimed it, “ the Mona Lisa of resonances”. We would like to thank Dr. A. Marwick of IBM T.J. Watson Research Laboratory for providing us with a
PI C. Rolfs and W.S. Rodney, Nucl. Phys. A235 (1974) 450. I31 K.M. Horn, WA. Lanford, K. Rodbell, and P. Ficalora, Nucl. Instr. and Meth. B26 (1987) 559. 141 W.A. Lanford and X.S. Guo, private communication. E51 W.A. Lanford, Solar Cells 2 (1980) 351. PI HA. Bethe, Phys. Rev. 55 (1939) 103 434. [71 W.A. Fowler and C.C. Lauritsen, Phys. Rev. 58 (1940) 192. PI A. Schardt, W.A. Fawler and C.C. Lauritsen, Phys. Rev. 86 (1952) 527. 191 A.A. Kraus Jr., A.P. French, W.A. Fowler, and CC. Lauritsen, Phys. Rev. 89(l) (1953) 299. WI D.F. Hebbard, Nucl. Phys. 15 (1960) 289. PII S. Gorodetzky, J.C. Adolff, F. Brochard, P. Chevalher, D. Disdier, Ph. Gorodetzky, R. Modjtahed-Zadeh and F. Scheibling, Nucl. Phys. All3 (1968) 221. WI F. Ajzenberg-Selove, Nucl. Phys. Al66 (1971) 38. 1131 F. Ajzenberg-Selove, Nucl. Phys. A281 (1977) 1. v41 W.A. Lanford, Nucl. Instr. and Meth. 149 (1978) 1. (151 P.H. La Marche, Ph.D. Thesis, Yale University (1981) (University Microfilms, Ann Arbor, Michigan). [=I B. Manrel and G. Amsel, Nucl. Instr. and Meth. 218 (1983) 159. M. Weiser, G. Heusser, S. Kalbitzer, [I71 H. D~j~tsc~tsch, and H. Mannsperger, Nucl. Instr. and Meth. 218 (1983) 129. WI A. Schardt, W.A. Fowler and C.C. Lauritsen, Phys. Rev. 86, (1952) 533.
8 [19] Applied
K.M. Horn, W.A. Lunford / Off-resonance cross section of the 6.4 MeV1H(15N,
Gamma-ray Spectrometry, C.E. Crouthamel, (Pergamon Press, New York 1970) pp. 202-205. [ZO] Nuclear Physics, W.E. 3~ch~, (Longmans Green and Co. Ltd., London 1963) pp. 144-145.
ayf2C
reaction
[21] Handbook of Numerical Analysis Applications, Jaroslav Pachner, (McGraw-Hill Book Company, New York 1984) 3.4-3.5 St P.130-P.131. [22] TRIM-88, J.F. Ziegler, J.P. Biersack, and G. Coumo, IBM T.J. Watson Research Laboratory, Yorktown Heights, NY.
Nuclear Instruments and Methods in Physics Research B34 (1988) 1-8 North-Holland, Amsterdam
MEASUREMENT OF THE OFF-RESONANCE CROSS SECTION OF THE 6.4 MeV ‘H(15N, c~y)‘~C NUCLEAR REACTION * KM. HORN and W.A. LANFORD
Received 4 January 1988
Measurements of off-resonance yield from the 6.4 MeV *H(15N, ay)“‘C nuclear reaction indicate that the off-resonance cross section is 77 pb, much smaller than the currently published value. A procedure for directly evaluating the off-resonance gamma-ray yield detected during hydrogen profiling measurementsis presented. The absolute on-resonance and off-resonance cross sections of this nuclear reaction are evaluated.
1. Intruduction Since the inception of the use of the 6.4 MeV rH(15N, ay)“C nuclear reaction as a tool for profiling hydrogen concentrations within solid targets [I], the cont~bution of yield from off-resonance reactions has been a concern. However, corrections to measured yields based on the published value of the off-resonance cross section [Z] have not agreed well with experimental data, often predicting yields in excess of those actually measured. Because of the difficulty in preparing a suitable hydrogen target for precise measurement of the off-resonance cross section (i.e. a thin, stable, hydrogen-rich surface layer covering a hydrogen-free backing), the cross section has ~sto~e~ly been determined using a thin r5N target and a proton beam. However, recent hydrogen profiling measurements we have made in hydrogen gas environments have highlighted the inaccuracy of the currently accepted value for the off-resonance cross section and prompted a more careful examination of it. In utilizing the rH(r5N, ~uy)‘~C nuclear reaction for detecting hydrogen, the target is bombarded with a beam of r5N ions at energies of 6.4 MeV and above. At 6.4 MeV (the reaction’s resonance energy) a reaction can occur between an incident nitrogen ion and a target hydrogen nucleus producing a characteristic gamma-ray of energy 4.43 MeV. A -g~a~ray detector is used to measure the yield of these characteristic gamma-rays. For a given number of incident r5N ions, this yield is directly proportional to the amount of hydrogen in the target at the depth at which the beam is at the resonance energy. When the energy of the incident r5N
(a)
I-
HYDROGEN-BEARING
LAYER
(b)
Fig. 1. Schematic representation of the (a) on-resonance and (b) off-resonance condition.
* Supported in part by a grant from IBM Corporation. ~~68-583X/88/$03.50 @ Elsevier Science ~blishers (North-Holland Physics Publishing Division}
beam is set to the resonance energy of 6.4 MeV, the measured gamma-ray yield results from reactions with hydrogen on the surface - see fig. la. At higher beam energies, the incident ions do not reach the resonance energy until they have penetrated some distance into the target, owing to stopping power effects. Therefore, as the beam energy is increased, the resonance probes successively deeper regions of the sample resulting in a profile of the hydrogen con~ntration in the target as a function of depth. When the resonance is deep within the target, a hydrogen-rich surface layer can interact with the incident beam of nitrogen ions through the off-resonance cross section - see fig. lb. Though this cross section is many orders of magnitude less than the on-resonance cross section, the gamma-ray yield from the interaction of a hydrogen-rich surface layer with the off-resonance cross section can rival or surpass the yield arising from the resonance cross section probing a region ~ntai~g little or no hydrogen‘
B.V.
2
KM. Horn, W.A. Lanford / Off-resonance cross section of the 6.4 MeV ‘H(‘%
Evidence of the inaccuracy of the currently accepted off-resonance cross section of 500 fib [2] became apparent during measurements of the hydrogen concentrations present at the interfaces of m~~ayered samples while these samples were in a 1 Torr hydrogen atmosphere (33. Contrary to expectations based on a cross section of 500 pb, we found that even in the presence of a huge hydrogen surface signal (corresponding to the 1 Torr of hydrogen gas surrounding the target) it was possible to probe thousands of ~ngs~~~ into a clean, untreated, single crystal of silicon with surprisingly high sensitivity. Nevertheless, a small, yet constant, extranwus gamma-ray yield was observed whenever targets were measured in a 1 Torr hydrogen atmosphere. ?Vhen the effect proved to be dependent only upon the hydrogen pressure in the gas cell, it became apparent that the additional yield was the result of an interaction of the gas-phase hydrogen with the off-resonance cross section. Though the effects of the off-resonance yield were clear, the unwieldy geometry of our gas cell precluded the precise determination of the off-resonance cross section using a gas-phase hydrogen target.
c~y)‘~C reaction
_-
II IC3
SC0
JOC
CHANNEL NUMBER
2. Experimental In order to gain the high statistical accuracy needed to arrive at au accurate value for the ‘H(15N, ory)i2C off-resonance cross section, we required a target with a large hydrogen concentration confined to a relatively thin layer of a few thousand tigstriims. The target also had to be stable under prolonged beam exposure (i.e. hundreds of nA over several hours}. Previous work done by Lanford and Guo [4] indicated that thin titanium films can be hydrated to a stoichiometry of approximately TiHa. Being both rich in hydrogen and stable under long ion beam exposures, titanium diiydride is an excellent target for this cross section measurement. The tit~ium dihydride target was made by evaporating pure titanium onto a clean silicon substrate at 10e6 Torr vacuum in a diffusion-pumped evaporation chamber equipped with resistive-hits evaporant boats. After the evaporation, the sample was annealed in a hydrogen atmosphere at 350 ’ C for 30 min. Once hydrogenated, the hydrogen content of the sample proved to be stable over many months and repeated exposures to the ion beam. Presented in fig. 2 is a c~~acte~~tion of the TiH,/Si(lOO) target used in determining the off-resonance yield correction. Fig. 2a is a Rutherford backscattering spectrum of the target showing it to be composed of a titanium layer with an underlying silicon substrate. Because Rutherford backscattering is iusensitive to elements of mass less than or equal to that of the incident projectile (helium ions, in this case) the hydrogen present in the sample is not detected. Fig. 2b is a hydrogen profile of this same target using the
fc)
BEAflENERGY
[Me'4
Fig. 2. Analysis of the TiH,/Si(lOO) target using (a) Rutherford backscattering and (b) hydrogen profiling. An expanded view of the off-resonance region is given in (c).
*H(“N, ~uy)“C nuclear reaction technique. Between the energies of 6.4 MeV and 7.05 MeV, the large hydrogen content of the titanium dihydride layer in the target is apparent. In profiling the off-resonance region from 7.25 to 8.0 MeV, the number of incident nitrogen ions per data point was increased by a factor of ten over that used to profile the hydrogen-rich titanium layer in order to increase the accuracy of the off-resonance yield measurement. Fig. 2e is an expanded depiction of this off-resonance region of the hydrogen profile shown in fig. 2b.
K.M. Horn, W.A. Lunford / Off-resonance cross section
ofthe 6.4
MeV ‘H(“N,
oiy)“C reaction
3
section might, in fact, arise from the interaction of the resonance with hydrogen deep in the bulk. Therefore, for comparative purposes, Fig. 3 displays the results when the same characterization techniques are applied to the back side of the silicon substrate which was protected from the titanium evaporation, but fully exposed during the hydrogen annealing. As is clear from fig. 3b, the only appreciable yield detected when profiling the back side of the silicon substrate is on the surface, the result of contamination from the ambient hydrocarbons in the vacuum of the analysis chamber. Within the silicon substrate essentially zero hydrogen is detected.
3. Correcting for off-resonance files
B-0
6.2
6.4
6.6
1.8
7.0
SEAM ENEAGY
72
7.4
7.8
7.8
D&VI
Correcting for off-resonance yield becomes a concern when measuring low concentrations of hydrogen in the interior of samples with overlaying layers which contain significant amounts of hydrogen. Such correction, however, is easily accomplished in the region in which the off-resonance cross section remains fairly constant (up to 8 MeV), by simply subtracting from the measured gamma-ray yield a number of counts proportional to the amount of hydrogen subject to the off-resonance cross section. This proportionality constant can be determined from the data of fig. 2b. Here, the area under the hydrogen bearing region of the hydrogen profile is 9.96 x lo6 keV . counts; the resulting average off-resonance yield is 127 (having corrected for the ten-fold increase in a~umulat~ charge with which the off-resonance data were taken). The number of counts arising from off-resonance yield when profiling past a hydrogen bearing layer, with integrated area I (expressed in keV . counts), is then simply: YOff-tes= (1.28 x 10-5)1.
BEAM ENERGY
[MeV]
Fig. 3. Analysis of the Si(100) side of the target using (a) Rutherford backscattering and (b) hydrogen profiling. An expanded view of the off-resonance region is given in (c).
It should be noted that the hydrogen profile measurements do not explicitly rely on measurements of the ‘H(“N, ory)“C reaction cross section. Rather, this hydrogen profiling technique was “calibrated” by measurements done on a variety of targets of known hydrogen content, including ion implanted samples [5]. In order to arrive at an accurate off-resonance yield correction, it is important that the amount of hydrogen in the substrate be zero or near-zero. Otherwise, the yield which we wish to ascribe to the interaction of the surface hydrogen layer with the off-resonance cross
yield in hydrogen pro-
(1)
The above correction formula was dete~n~ from measurements in which a 3 x 3 in. bismuth germanate (BGO) gamma-ray detector was positioned at 0 o to the incident ion beam and separated from the target by 2.5 cm. For other geometries, the correction constant derived from the ratio of the on-resonance to off-resonance yield must be adjusted to compensate for the differences in the angular dependence of gamma-ray emission of the on-resonance and off-resonance reactions. To illustrate this point, it can be seen from the angular distribution of gamma-rays presented in fig. 4 that the ratio of the on-resonance to off-resonance yield measured at 0” is more than twice as large as that measured at a beam-detector angle of 45 O. Though knowledge of the precise value of the on-resonance and off-resonance cross sections of the ‘H(r’N, cyy)“C nuclear reaction is not necessary in
K.M. Horn, WA. Lanford / Off-resonance cross section of the 6.4 MeV ‘H(-“N, cuy)12C reaction
the *‘N(p, cuy)*‘C resonant reaction and determined the probability of emission of a gamma-ray at an angle B to the incident proton beam to be, Bq 0) = [: + :cos2e - $cos‘q +&[1-3
n.31
OFF-RESONANCE 0 = 40 iJc i 1 i ,=-R-.-.-.-I-.-D-.-.--8 i
0
50
100
BEAM - DETECTOR ANGLE
150
[degrees]
Fig. 4. Comparison of the angular distribution of gamma-rays emitted by the 6.4 MeV ‘H(15N, ay)12C on-resonance and off-resonance nuclear reactions.
order to estimate and correct for the effects of off-resonance yield in hydrogen profiling measurements, the
TiH, target created for this experiment lends itself nicely to such a determination. Furthermore, the long history of measurements of the cross section of this nuclear reaction and revisions to its accepted FWHM make its re-examination desirable. To this end, on-resonance and”off-resonance gamma-ray yields were measured from a second, somewhat thinner TiH, target mounted in an experiment chamber which allowed precise measurement of the various parameters necessary to determine the reaction’s absolute cross sections.
cos2e + 4 co&q,
(2)
where x = 0.82 for the 429 keV resonance. In the ensuing years, the 429 keV resonance was m-examined in several works [lo-131 with no revisions of the accepted cross section or FWHM reported. In 1974, Rolfs and Rodney [2] presented a comprehensive examination of both the 15N(p, y)r6 0 and 15N(p, cyy)12C nuclear reaction cross sections. In this work, which showed that the 15N(p, cyy)r2C nuclear reaction makes only a negligible contribution to hydrogen burning at stellar energies, an above-resonance off-resonance cross section of approximately 500 pb (fig. 7a) was reported. With the application of the inverse 6.4 MeV ‘H(15N, ay)12C reaction to the measurement of hydrogen in solids in the mid-1970’s [l], it became apparent that the FWHM of the resonance was narrower than the 13.5 keV cited in the literature. A succession of lower values for the FWHM of the resonance were reported by several authors from 1976 to 1980 [14,15]. In 1983, Maurel and Amsel 1161 and Damjantschitsch, et al. [17] independently measured the FWHM of the resonance to be 1.8 keV. Taking the product of the historically accepted cross section (300 mb) and FWHM (13.5 keV) to be invariant, this new measurement of a FWHM of 1.8 keV implies a total on-resonance cross section of 1.6 b.
5. Determination of the 6.4 MeV ‘H(15N, aty)“C cross section
4. Previous measurements
of the ‘H15N, cuy)“C cross
section
Study of this nuclear reaction’s cross section began in the late 1930s as a part of the investigation of the carbon-nitrogen-oxygen cycle of stellar energy generation proposed by Bethe [6]. Fowler and Lauritsen [7] performed the earliest measurements of the 15N(p, (uy)12C reaction in 1940 by bombarding an enriched 15N target with protons; they reported the presence of resonant reactions at 0.88, 1.03 and 1.20 MeV. A more detailed investigation of the reaction by Schardt, Fowler, and Lauritsen [S] in 1952 detected a resonance at 429 keV with a measured on-resonance cross section of 300 mb and a full width at half maximum (FWHM) of 0.9 keV. For the inverse 6.4 MeV ‘H(15N, q)i2C reaction, in which a beam of “N ions is incident on a hydrogen-bearing target, the corresponding FWHM is 13.5 keV. The following year, Kraus, et al. [9] measured the angular distribution of gamma-rays resulting from
The total yield from a nuclear reaction experiment is given in its most general form as, Y=Nin,a(E)~,
(3)
where Ni is the number of incident ions, n, is the area1 density of the nuclei in the target, a(E) is the reaction’s total cross section, and e is the source intrinsic efficiency of the detector. The yield measured in a solid angle, Ati, at a specified angle, 8, to the incident beam is simply, Y(E,
8) = Nin,
do(E,
B)rAS2,
(4)
where do(E, 19) is the differential cross section of the reaction at energy E and angle 0 and the term eA0 is the incident intrinsic efficiency of the detector. The number of incident ions, Ni, can be expressed as the total amount of charge incident on the target divided by the charge of each individual incident ion, Q/q. For a target of arbitrary hydrogen content versus depth, the yield can be thought of as arising from a series of thin
5
K.M. Horn, W.A. Lanford / Off-resonancecrosssectionof the 4.4 MeV ‘H(“N, ay)12C reaction target slabs each of uniform hydrogen content, p(x). The total yield measured over a solid angle AP at an angle 0 to the incident beam can then be expressed more explicitly as the yield arising from each slab of thickness dx, summed over the entire thickness of the target, t. Y(E,
dx] du(E,
@)=jd[$][p(x)
B)EAL?.
5.1. Off-resonance cross section In applying eq. (5) to the off-resonance condition, it can be recognized that the differential cross section, d u( E, 8), is essentially constant over the energy range of 6.5-8.0 MeV and can thus be factored out of the integral. 8) = $A0
da(E,
B)ldp(x)
dx.
(6)
For a target of uniform or slowly varying hydrogen concentration, pH is a constant which can likewise be factored out of the integrand, the yield equation simplifing to: Y(E,
0) = +AP
da(E,
@pt.
2 >
.
.
500
ti
.
.
.
i
i
(5)
As has been shown in the literature, the on-resonance cross section of the 6.4 MeV ‘H(15N, cyy)“C nuclear reaction is sharply peaked about its resonance energy, possessing a Lorentzian-shaped excitation curve as described by the Breit-Wigner dispersion formula [18]. On the other hand, the off-resonance cross section averaged over the target thickness is relatively constant upto energies of 8.0 MeV, as can be seen from fig. 2c. Furthermore, the angular distribution of gamma-rays resulting from the on-resonance reaction, depicted in fig. 4, is distinctly different from that of the off-resonance reaction which exhibits only the weakest of angular dependency. Because of the differing natures of the on-resonance and off-resonance cross sections, the yield equation for each must be derived separately.
Y(E,
5loooi
(7)
In evaluating the off-resonance cross section, gamma-ray yields were measured from a 1800 A titanium dihydride layer using a 3 X 3 in. BGO detector, positioned three inches from the sample. These measurements were made at various angles relative to the incident ion beam, ranging from 0 o to 90 o in 15 o steps (see fig. 5). In this geometry, the detector’s incident intrinsic efficiency, eAO, is 0.241 [193 for the combined full energy and single escape peaks; the areal density of hydrogen in the TiH, layer, pHt was determined to be 1.92 x lOIs H/cm* through application of an empirical formula determined from measurement of hydrogen standards [5]. A total integrated charge, Q, of 80 PC was collected for each data point using a doubly ionized “N beam
BEAM - DETECTOR
ANGLE
[degrees]
Fig. 5. Measurement of the off-resonance gamma-ray yield from the 6.4 MeV ‘H(i5N, cyy)12C nuclear reaction. Target-detector distance is 3 in., integrated charge is 80 pC.
(therefore, q = 3.204 x lo-l9 C). Utilizing the off-resonance yield measurements presented in fig. 5, the differential cross section at 0 o is calculated to be 4.76 pb. Dividing this value by the solid angle subtended by the detector, 0.212a, the differential cross section per steradian at 0’ is 7.15 pb/sr. After calculating these values for each of the other data points, the total cross section, u, is determined by integrating the differential cross section per steradian over all angles [20]: U=
257
/.i0
sdu(Ey 0)
sb
0
de
dq
dG
0
Assuming no azimuthal dependence of the reaction’s gamma-ray emission, the integral over cp evaluates to 2a. The integral over 0 is evaluated numerically using modified, composite Simpson rule [21] over the range 0 = 0 to 7r/2. The gamma-ray yield measurements made at beam-detector angles varying from 0 o to 150 o (fig. 4) show no indication of any asymmetry about r/2 so, the result of the integration over this region is simply doubled to evaluate the limits 0 to a. The total off-resonance cross section at 7.4 MeV is calculated to be 77 pb. The result at this energy and several other energies is presented in fig. 7b. 5.2. On-resonance cross section Beginning again from the general yield expression of eq. (5), those variables that are kept constant during the experiment can be factored out of the integral leaving, Y(E,
0) = +APJoidu(E;
B)p(x)
dx.
(9)
The integral, which is initially over target thickness x, is converted to one over energy through the change of variable, dE dx = dE/dx
’
K.M. Horn, WA. Lmjord / Off-resonance cross section of the 4.4 MeV ‘H(“N, cuy)12Creaction
6
For a sufficiently thick target (i.e. one from which the ion beam does not exit) the energy of the “N ions within the target range from E = E,, the energy of the ion beam at the surface, to E = 0, after the ions have come to rest within the target. The yield equation then takes the form,
For a hydrogen distribution which is constant or slowly varying within the target, p,(E) can be taken to be constant over the energy range of this narrow resonance. The stopping power, dE/dx, which is also a function of energy, is likewise treated as constant over the energy range of the narrow resonance. Since the ions’ energy decreases with increasing depth, dE/dx is negative. In order that we may treat dE/dx as a positive value, the implicit negative sign will be absorbed into the integral by reversing the limits of integration. Extracting the constant terms from the integrand results in the yield equation:
Y(E, f3)=$rAPp c&&~Bdo(E,
@>dE.
(11)
The form of the resonant cross section given by the single level Breit-Wigner dispersion formula is [X3], da(E,B)
P/4
=da(E,, 0)
(12) (E-Er)'+T2,'4'
Substituting this expression into eq. (11) gives, Y(E,
e) =
$rA9p
X
EB
J0
n&d+&,
0)
r2/4
dE
’
(E-E,)2+T2/4
(13)
where do(E,, 0), the differential cross section of the reaction at the resonance energy of 6.4 MeV, is a constant that has been brought outside the integral. Evaluation of the integral results in a yield equation of the form,
Y(E, 0) = $AQ
du(E,,
e)P,&--;
O-
In the thick target approximation it is assumed that the resonance reaction occurs deep within the target; the beam energy, therefore, is taken to be very large, i.e. E, = co.For this narrow resonance, r/2 < EB - Er and r/2 << E,, so to a very good approximation, tan-‘( EB-Er)/(T/2)=a/2 and tan-‘(E,)/(T/2) = -CT/~.Eq. (14) then simplifies to:
60
BEAM - DETECTOR ANGLE
90 [degrees]
Fig. 6. Measurement of the on-resonance gamma-ray yield from the 6.4 MeV rH(“N, cuy)r’C nuclear reaction. Target-detector distance is 5 in., integrated charge is 4 pC.
In order to use this expression to determine the differential cross section, and ultimately the total cross section, gamma-ray yields were measured on the TiH, target with the BGO detector mounted five inches from the sample over a range of beam-detector angles ranging from 0 o to 90° (see fig. 6). Because the on-resonance yield from this reaction is so large, the detector was positioned further from the target than in the off-resonance measurement to better resolve the angular dependence of the emitted gamma-rays. As is apparent from the functional form of the angular distribution of emitted gamma-rays developed by Kraus, and as suggested by the measurements presented in fig. 4, the angular distribution of gamma-rays is an even function and therefore is symmetric about r/2, thus alleviating the need to measure beyond 90 o _ Each data point was measured with a collected charge of 4 PC, using a doubly ionized 15N beam. The detector’s incident intrinsic efficiency,
-tad+ 1. (14) -E
30
K.M. Horn, W.A. Lanford / Off-resonance cross section of the 6.4 MeV ‘H(“N,
ay)“C
reaction
7
6. Discussion The motivation for the present experiment was to obtain an accurate procedure for determining the number of counts observed in a hydrogen profiling measurement that are due to off-resonance reactions. Eq. (1) gives this contribution to the count rate for a 3 X 3 in. BGO detector mounted at 0 o to the incident ion beam. We believe that over our energy range (6.4-8.0 MeV) this expression is accurate to 15% or better. Since this contribution is so small, in most cases, this is more than accurate enough for hydrogen profiling purposes. The on-resonance cross section measurement m”ade in this work agrees quite well with the historically derived value, On the other hand, the off-resonance cross section of 77 gb measured in this experiment differs greatly from the literature value of 500 pb [2]. While it is difficult to know for certain why past measurement of this cross section resulted in such a large value, it is possible that this was due to a low energy tail in the proton beam. It is well known that unless great care is taken (polishing slits, antiscattering slits, etc.) proton beams can exhibit low energy tails with intensities of order lop3 to 10e4 of the total beam intensity. In the presence of such low energy tails, yield from low energy ions interacting on-resonance with the 15N target would simulate the off-resonance reaction. In contrast, N15 ion beams, because of their large stopping power, have very small low energy tails.
15NBEAM ENERGY jMeV1
j5NBEAM ENERGY [MeVl
Fig. 7. Total cross section of the 6.4 MeV resonance of the rH(15N, cyy)“C nuclear reaction (a) 1974 and (b) 1988. The resonance width of 1.8 keV depicted in (b) reflects the values
measured by Maurel and Amsel [16] and Damjantschitsch et al. [17].
computer program for calculating gamma-ray detector efficiencies.
References
PI W.A. Lanford, H.P. Trautvetter, J. Ziegler, and J. Keller, Appl. Phys. Lett. 28 (1976) 566.
7. Conclusion As is contrasted in fig. 7, over the past five years, the measured value of the cross section of the 6.4 MeV ‘H(15N, ocy)i2C nuclear reaction has changed dramatically. Maurel and Amsel[16] as well as Damjantschitsch et al. [17], in 1983 measured the FWHM of this resonance to be 1.8 keV, implying an on-resonance cross section of 1.6 b. In this work we have explicitly measured this cross section to be 1.56 b. The off-resonance cross section measurement of 77 pb is much less than the literature value of 500 p’b. The ratio of the on-resonance to off-resonance cross section is then 20800 - almost seven times greater than the most recent estimate [17]. As shown in fig. 7b, the cross section of the 6.4 MeV lH(r’N, ay)“C resonance changes over four orders of magnitude from on-resonance to off-resonance on either side, with a full width at half maximum of only 1.8 keV, making this one of the most aesthetically pleasing resonances in nature - or as G. Amsel has proclaimed it, “ the Mona Lisa of resonances”. We would like to thank Dr. A. Marwick of IBM T.J. Watson Research Laboratory for providing us with a
PI C. Rolfs and W.S. Rodney, Nucl. Phys. A235 (1974) 450. I31 K.M. Horn, WA. Lanford, K. Rodbell, and P. Ficalora, Nucl. Instr. and Meth. B26 (1987) 559. 141 W.A. Lanford and X.S. Guo, private communication. E51 W.A. Lanford, Solar Cells 2 (1980) 351. PI HA. Bethe, Phys. Rev. 55 (1939) 103 434. [71 W.A. Fowler and C.C. Lauritsen, Phys. Rev. 58 (1940) 192. PI A. Schardt, W.A. Fawler and C.C. Lauritsen, Phys. Rev. 86 (1952) 527. 191 A.A. Kraus Jr., A.P. French, W.A. Fowler, and CC. Lauritsen, Phys. Rev. 89(l) (1953) 299. WI D.F. Hebbard, Nucl. Phys. 15 (1960) 289. PII S. Gorodetzky, J.C. Adolff, F. Brochard, P. Chevalher, D. Disdier, Ph. Gorodetzky, R. Modjtahed-Zadeh and F. Scheibling, Nucl. Phys. All3 (1968) 221. WI F. Ajzenberg-Selove, Nucl. Phys. Al66 (1971) 38. 1131 F. Ajzenberg-Selove, Nucl. Phys. A281 (1977) 1. v41 W.A. Lanford, Nucl. Instr. and Meth. 149 (1978) 1. (151 P.H. La Marche, Ph.D. Thesis, Yale University (1981) (University Microfilms, Ann Arbor, Michigan). [=I B. Manrel and G. Amsel, Nucl. Instr. and Meth. 218 (1983) 159. M. Weiser, G. Heusser, S. Kalbitzer, [I71 H. D~j~tsc~tsch, and H. Mannsperger, Nucl. Instr. and Meth. 218 (1983) 129. WI A. Schardt, W.A. Fowler and C.C. Lauritsen, Phys. Rev. 86, (1952) 533.
8 [19] Applied
K.M. Horn, W.A. Lunford / Off-resonance cross section of the 6.4 MeV1H(15N,
Gamma-ray Spectrometry, C.E. Crouthamel, (Pergamon Press, New York 1970) pp. 202-205. [ZO] Nuclear Physics, W.E. 3~ch~, (Longmans Green and Co. Ltd., London 1963) pp. 144-145.
ayf2C
reaction
[21] Handbook of Numerical Analysis Applications, Jaroslav Pachner, (McGraw-Hill Book Company, New York 1984) 3.4-3.5 St P.130-P.131. [22] TRIM-88, J.F. Ziegler, J.P. Biersack, and G. Coumo, IBM T.J. Watson Research Laboratory, Yorktown Heights, NY.