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Low energy nuclear cross sections in metals
Surface & Coatings Technology 201 (2007) 8574 – 8578 www.elsevier.com/locate/surfcoat
Low energy nuclear cross sections in metals Jirohta Kasagi Laboratory of Nuclear Science, Tohoku University, Mikamine 1-2-1, Taihaku, Sendai 982-0826, Japan Available online 13 March 2007
Abstract In order to investigate the interplay between nuclei and their surroundings, deuteron induced fusion reactions in a metal environment have been studied at very low energies. We summarize the results of the measurements so far performed: reaction rates of the D(d,p)T reaction in various metals and those of the 6,7Li(d,α)4,5He reaction in Pd and Au. In addition, the kinematic measurements recently performed are also described. These measurements showed that low energy nuclear reactions are strongly affected by the metal environment and huge amounts of energy in the condensed matter scale might be converted to the colliding two-body system. © 2007 Elsevier B.V. All rights reserved.
1. Introduction Effects of the surroundings of a nucleus on nuclear phenomena have been investigated for many years [1]. Usually the observed effect is very small, less than 1% at most. Such smallness is due to the huge difference of the interaction energies; i.e., eV in an atomic system, versus MeV in a nuclear system. However, a surprisingly large effect was claimed in the so-called cold fusion [2], which roused attention more strongly on the influence of the environment where nuclear processes take place. Since then, enhancement of the reaction rates of the D + D reaction during implantation of deuterium in metal has been intentionally searched for. Roth et al. [3] first reported the reaction rate of the D + D → p + t reaction in Ti down to Ed = 3 keV and showed that the deduced excitation function is consistent with no enhancement in the cross section. Kasagi et al. [4] measured the thick target yields for the D(d,p)T and D(d,n)3He reactions in Ti for 4.5 b Ed b 18 keV, and concluded that they were explained well by the cross sections of the data compiled by Bosch and Hale [5]. Yuki et al. [6] succeeded in measuring the reaction rates at lower bombarding energies down to 2.5 keV, and deduced the screening energy of the DD reaction in metal, which is a quantitative scale of the enhancement at very low energies. The screening energy for Yb host (80 eV) is the first evidence for enhanced fusion reaction rate in the metal environment for the keV deuteron bombardment.
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Anomalously large values of screening energy were found later for PdO (600 eV), Pd (310 eV) and Fe (200 eV) [7]: the reaction rate for PdO at Ed = 2.5 keV is about 100 times the normal. Such large screening energies for the DD reaction were also found in other materials by other groups. Czersky et al. [8] reported enhanced screening energy of the DD reactions in Ta; it was about 300 eV, and was confirmed by Raiola et al. [9] Ichimaru et al. [10] suggested that hydrogen nuclei in metal are strongly screened, since the electrons both in the metallic dband and the hydrogen induced s-band can contribute to the screening effect. They calculated the effective static potential for hydrogen in Ti and Pd, and proposed that the screening distance between two hydrogen nuclei in metal is much shorter than that for atomic hydrogen. However, the calculated screening energy is only 51 eV for Ti and 75 eV for Pd. Czerski et al. [11] calculated the screening energy for DD reactions in metal by applying a dielectric functional method. Their results including the cohesion effects give larger values of the screening energy in a metal environment, for example about 130 eV for Pd, but less than half of the observed value. One can thus summarize the present situation as follows. Low energy DD reactions are enhanced very much when the reaction occurs in a metal environment. The enhancement may be described by a screening energy and depends strongly on the host material. The mechanism of enhancement is not fully understood, especially for the environment which provides screening energy of the DD reaction of more than 200 eV. All these arguments raised the motivation of further studies to
J. Kasagi / Surface & Coatings Technology 201 (2007) 8574–8578
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parameters. Greife et al. [17], reported measurement at centerof-mass energies down to 1.6 keV and deduced the screening energy to be 25 eV, which is considered to be due to the bound electron, and is consistent with a simple estimation described above as well as an estimation based on a quantum picture. Thus one can say that the screening energy of the DD reaction for a D2 gas target is well understood to be due to bound electrons. 3. D + D reactions in metals 3.1. Experimental method
Fig. 1. Relative yield of protons emitted in the D(d,p)T reaction in five hosts as a function of the bombarding energy; (a) two independent measurements for PdO, (b) for Pd and Fe, and (c) for Au and Ti. In the upper sections, the data normalized to the yield at 10 keV are plotted. In the lower sections, the experimental yields divided by the standard calculations are shown as enhancement factor.
understand the phenomena fundamentally as well as to develop applications. 2. Screening energy of D + D reaction with gas target At energies far below the Coulomb barrier, cross sections of nuclear reactions are essentially dominated by the Coulomb penetration factor [12,13]. However, there are significant cross section enhancements beyond the prediction of barrier penetration [14–18]. These enhancements are qualitatively understood as a screening effect due to bound electrons. In a naive picture, the screening effect may be described quantitatively by a screening energy Us, and the cross section at the center-of-mass energy Ecm is described as rðEcm Þ ¼
S ðEcm Þ expf2pgðEcm þ Us Þg; Ecm
ð1Þ
where S(E) is an astrophysical S-factor, and η(E) = ZTZpα(μc2/ 2E)1/2 is the Sommerfeld parameter; ZT and Zp are atomic numbers of the target and projectile, α is the fine structure constant and μ is the reduced mass. The greater the value of Us, the greater the enhancement and vice versa. D + D reactions have been investigated with gas targets by many authors. Krauss et al. [19], parameterized the S-factors for the D(d,p) and D(d,n) reactions by fitting their data with a quadratic polynomial for 5 b Ecm b 120 keV. Bosch and Hale [5] parameterized the reaction cross sections by using the R-matrix
In order to measure the DD reactions below 10 keV, a high current beam is necessary because the cross sections are very small. We have performed such experiments using a low energy ion beam generator at the Laboratory of Nuclear Science of Tohoku University, as described in our previous work [6,7]. Up to the present, we have measured D + D reactions as a function of bombarding energy between 2.5 and 10 keV to deduce the reaction rates. Various foils were bombarded as host materials, such as Be, Ti, Fe, Cu, Ni, Pd, Sm, Yb, Au and PdO. Protons emitted in the D(d,p)T reactions were detected with a ΔE − E counter telescope consisting of 50- and 200-μm thick Si surface barrier detectors. During measurement at a specific bombarding energy, the yield at 10 keV was measured very frequently at intervals in order to verify the number of target deuterons. We always normalized the proton yield to that at 10 keV measured just before and after the run. 3.2. DD fusion in metals In Fig. 1 we show the relative excitation functions of the D(d,p) T reaction in PdO, Pd, Fe, Au and Ti, to demonstrate that the reaction rates depend strongly on the host materials. As expected from the bare D + D reaction the yields decrease very rapidly as the bombarding energy decreases. We show the standard yield by a dotted curve, which corresponds to the thick target yield calculated for the bare D + D reaction in materials by the following equation. Z Ed Yp ð E d Þ ¼ A ND ð xÞrð E Þð dE=dxÞ1 dE; ð2Þ 0
where σ(E) is the bare cross section parameterized by Bosch and Hale [5] and (dE/dx) is the energy loss curve of deuteron Table 1 Screening energy of the D + D reaction in metals obtained from our measurements Material
Screening energy (eV)
PdO Pd Fe Re Cu Yb Ni Au Ti
600 ± 30 310 ± 30 200 ± 20 200 ± 20 120 ± 20 80 ± 20 80 ± 20 70 ± 20 65 ± 30
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parameterized by Anderson and Ziegler [20]. The yields at lower energies depend on the host material very strongly. In the lower part of Fig. 1, we plot the ratio of the experimental yields to the standard calculation in order to make comparisons more clearly. As seen, the reaction rate in PdO is enhanced very much, whereas the deduced enhancement is very small for Au and Ti. In a naïve picture, the screening effect may be described quantitatively by a screening energy Us and the enhanced cross section is described in Eq. (1). The value of Us so far obtained in our measurements are listed in Table 1. Conduction electrons in metal can be regarded as a Fermi gas moving in a mean field produced by the lattice atoms and electrons. If a nucleus is placed in such an electron sea, the scalar potential produced by the nucleus is screened by the surrounding electrons. The Thomas–Fermi model gives ϕs(r) = Ze / r exp(− ker), where ke is given with the electron density ne and Fermi energy EF as ke = (6πe2ne / EF)− 1/2. The potential can be approximated as ϕs(r) = Ze / r − Zeke for ker ≪ 1, and, thus the screening energy for deuterons in the conduction electrons is estimated as Us = e2ke. The screening energy for a deuteron in the conduction electrons in Fe is estimated as Us = 24 eV in this picture; the value is only 1/10 of the experimentally deduced value. For Pd, Ichimaru et al. [10], including the effects of deuterons in the lattice, calculated the screening energy as Us = 75 eV. The experimental value is about 4 times larger than the calculation. Czerski et al. [11] calculated the screening energy for Pd to be 130 eV, less than half of the experimental value. Thus we conclude that the screening energy for DD fusion reactions in Fe, Pd and PdO cannot be explained by the presently available calculations. It should be stressed that those values are extraordinarily large; i.e., 310 eV for Pd and 600 eV for PdO. A relevant correlation may be that between the screening energy and the deuteron density in the host during bombardment: a large screening energy goes with a small density. In Fig. 2, we plot screening energy vs. inverse of deuteron density, including the data obtained by Rolf's group. The squares are our data [7] and the circles are those of Ref. [21]. Although the data are greatly scattered, a correlation between the screening energy
Fig. 3. Yield ratio of protons to tritons of the D + D→p + t reaction in Au (b), Pd (c) and PdO (d) detected at 145° for bombarding energies between 8 and 20 keV. In (a) the calculated results are shown for the assumption that the target deuteron is in motion toward the beam direction with various kinetic energies from 0 eV to 500 eV. A hatched region indicated in (b), (c) and (d) correspond to the estimated ratio including multiple scattering process.
and the deuteron density may be seen. It should be noted that correlations are clearly seen for the data indicated by larger circles and squares connected by arrows, which are for the same host metal but different density. It should also be pointed out that Pd and its hetero compound always show huge screening energy as follows: 310 eV [7], 800 eV [22], 300 eV [11] and 600 eV [7] for PdO. The density may be related to the diffusivity, or mobility of D+ ions in the host; large mobility results in small density of the target deuterons and large screening energy. We suggest the possibility of a dynamic screening mechanism during the deuteron bombardment and penetration into the host wherein the fluidity of deuterons must play a decisive role. 3.3. Kinematic measurement of the D + D→p + t reaction in metal Since the screening energy for the DD reaction in metals is much larger than the energy scale of the atomic systems, one might expect effects on the kinematic quantities. We have tested the possibility of seeing such an effect in yield ratios of protons to tritons in the D + D→p + t reaction detected with a single detector. The measured ratio is equal to the ratio of the solid angle ratio of protons to tritons which depends only on the bombarding energy as well as the detection angle, shown as follows;
Fig. 2. Screening energy vs. inverse of deuteron density. Our data are plotted with squares and the data reported in [8] are plotted with circles. A pair of large circle and square connected with an arrow is for the same host metal.
ðdr=dXcm Þp ðdXcm =dXlab Þp dNp =dXlab Yp R¼ ¼ ¼ Yt ðdNt =dXlab Þ ðdr=dXcm Þt ðdXcm =dXlab Þt ðdXcm =dXlab Þp ¼ : ðdXcm =dXlab Þt
ð3Þ
J. Kasagi / Surface & Coatings Technology 201 (2007) 8574–8578
Here, (dσ/dΩcm) is the differential cross section at the detected angle in the cm system and its value is the same for protons and tritons for the D + D → p + t reaction. Thus any deviation of the yield ratio from the kinematic calculation requires a change of the kinematics of the two-body colliding system; for example, the target deuteron is not at rest but in motion before the collision. Yield ratios of protons to tritons have been measured with a Si detector placed at 145° with respect to the beam direction for bombarding energies between 8 and 20 keV. Foils of CD2, Ti, Pd, PdO and Au were bombarded as the host for the DD reaction. In order to obtain statistically significant results, both protons and tritons were accumulated at least 40,000 counts for one run at each bombarding energy and more than 10 runs of the measurements were performed for each foil. In Fig. 3, we show the data for Pd, PdO and Au compared with a preliminary estimation including the multiple scattering, which is shown by the hatched area. Although the multiple scattering reduces the ratio considerably, the data cannot be explained by the estimated values. The largest deviation is observed for PdO shown in Fig. 3(d). We infer that the deviations from the calculation including multiple scattering are due to the motion of the target deuteron in the metal environment. The ratios calculated with a simple assumption that the target deuteron is in a linear motion toward the beam direction are plotted in Fig. 3(a), for kinetic energies of the target deuteron, 0, 50, 100, 300 and 500 eV. It should be noticed that the effect is not negligible but observable even for the energy of 50 eV. Although a precise calculation including multiple scattering is not available yet, the size of the deviation observed in Fig. 3(b), (c) and (d) roughly gives the amount of the kinetic energy of the target deuteron as follows; 50 eV for Au, 150 eV for Pd and 300 eV for PdO. Of particular interest is the correlation of the screening energy and the energy of the target deuteron. Thus, the large screening energy and the motion of the target deuteron might originate from the same source. 4. Screening energy for the Li + D reaction in metal In order to explore the mechanism of enhanced screening, other nuclear reactions have been measured in metal. We have investigated the 6,7Li(d,α)4,5He reactions in metal, for the first time [22]. We selected two metals as hosts in which the Li + d reactions occur; they are Pd and Au. As discussed in the previous section, the screening energy of the D + D reaction in Pd is very large. On the other hand, normal size of screening is obtained for the D + D reaction in Au as Us = 70 ± 10 eV in [7] and 61 ± 20 eV in [21]. The results for the PdLix and AuLix targets are shown in Fig. 4; Fig. 4(a) for PdLix and Fig. 4(b) for AuLix. The upper part of Fig. 4 shows the excitation functions of the 6,7Li(d,α)4,5He reactions relative to the yield at Ed = 75 keV. The standard calculations are plotted with dotted lines in Fig. 4. In the lower part of Fig. 4, we plot the ratio of the experimental yields to the standard calculations in order to make the comparison easier. As seen, the reaction rate in Pd is systematically enhanced for both reactions.
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Fig. 4. Relative yield of α particles emitted in the 6,7Li(d,α)4,5He reaction as a function of the bombarding energy of deuterons; (a) for PdLix and (b) for AuLix. In the upper part, the data normalized to the yield at 75 keV are plotted. In the lower part, the experimental yields divided by those presented with the dotted curve are shown. The dotted curves correspond to the relative yields calculated without screening. Solid curves correspond to calculations with the screening energy indicated in each section.
We deduced the values of Us of the 6Li(d,α)4He and the 7Li (d,α)5He reaction, separately, for each data by fitting the experimental relative yields. The results are Us = 1500 ± 310 and 60 ± 150 eV for the Li + d reactions in Pd and Au, respectively. The calculations with screening energy Us are shown by the solid lines in the upper and lower parts of Fig. 4. The screening energy of the 6Li + d and 6,7Li + p reactions has been obtained in [23] to be 420 ± 120 eV for the LiF target and 350 ± 80 eV for the hydrogen and deuterium gas target. The present work shows, for the first time, that, in a metallic environment, the size of the screening effect in the Li + d reaction depends strongly on the metal host. The obtained value of the screening energy in Pd is about 4 times larger than those mentioned above. As discussed in the previous section, the screened electrostatic potential of the nucleus with atomic number Z existing in the sea of conduction electrons is given as ϕs(r) = Ze / r·exp (− ker); ke = (6πe2ne / EF)1/2, ne is the number density of electrons and EF is the Fermi energy of the electrons. Thus the beam deuteron experiences a reduced Coulomb repulsion force, when
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it collides with the nucleus, and the corresponding screening energy is approximated as Uce = Ze2ke. For the Li + d reaction in Pd metal, EF = 2.66 eV and ne = 1.97 × 1022 cm− 3, thus Uce = 61 eV is expected. The effect of the bound electron should be added, since the Li atom is considered to remain in metal in the form of Li+. Summing up the values of the screening energy due to conduction electrons and bound electrons, we obtain a value of about 230 eV. Even if the experimental value in [12] is used for the bound electrons, the summed value is 410–480 eV. Therefore, the large screening energy of ∼ 1500 eV obtained for the Li + D reaction in Pd cannot be due to electron screening alone. Of particular interest is the fact that the Pd metal provides a large screening effect not only for the Li + d reaction but also for the D + D reaction, whereas the Au metal host does not in both cases. Thus the mechanism of enhanced screening in metal might have the same origin in the D + D and Li + d reactions. Although the enhanced screening is not fully understood, we have previously discussed the possibility that the large screening effect might originate from fluid deuterons in Pd. 5. Summary and outlook Low energy deuteron beams have been used for the study of nuclear fusion reactions in metal environment, since so-called cold fusion was claimed in this environment. Mostly studied is the D + D reaction, in which the implanted deuterons serve as targets for subsequent bombardment with other deuterons. Up to the present, there have been a few discovery steps which bring a significant surprise and raise considerable interest. The first is the fact that the DD reaction rate really depends on the host metal, which was reported in Ref. [6] although the observed change is not very large but certainly larger in Yb than in Ti. The second is the discovery of an anomalously large screening energy for Pd and PdO [7]. The other two groups subsequently and independently found a similar size for the enhanced screening for other metals. Thus one could conclude that D + D reactions in metal can be enhanced immensely and begin a serious exploration of nuclear fusion at room temperature. The screening mechanism so far studied in nuclear-astrophysics cannot explain the reported large screening energies. Therefore other factors to change the reaction rate should be searched for. This might originate from the condition of the surface, temperature of the beam spot, deuteron density, and so on. Experimental development together with theoretical progress is further desirable to reveal the nuclear reaction mechanism in condensed matter. Recent experiments on the Li + D reaction in metal is the first step for expanding nuclear reactions other than the D + D
reaction. The result is very interesting, because the reaction rate is enhanced very much for the Pd host as the D + D reaction. The kinematic measurement of the D + D reaction, which is performed quite recently by our group, gives a convincing result. It clearly shows that deuterons in Pd and PdO gain kinetic energy. It should be emphasized that the method of measuring the yield ratio does not require precisely constancy of the number of target deuterons: this condition is highly desired for the yield measurement. The observed large energy transferred to the motion of target deuterons might originate from the same source of the large screening energy, since there is strong correlation. Nuclear reaction studies with low energy deuteron bombardment on metal surfaces have revealed interesting features of reactions in metal: i.e., large energy transfer from condensed matter to the nuclear system. The large screening energy deduced for the DD reaction in Pd and PdO enables an occurrence of reaction with thermal energy deuterons, if the same condition was made. The large kinetic energy of the target deuteron, again, in Pd and PdO might help to understand the origin of the large screening energy. Further investigations serve to increase our fundamental understanding and to develop many applications. References [1] G.T. Emery, Annu. Rev. Nucl. Sci. 22 (1972) 165. [2] M. Fleischmann, S. Pons, J. Electroanal. Chem. 261 (1989) 301; S.E. Jones, et al., Nature 338 (1989) 737. [3] J. Roth, et al., Nucl. Fus. 30 (1990) 441. [4] Kasagi, et al., J. Phys. Soc. Jpn. 64 (1995) 3718. [5] H.S. Bosch, G.M. Hale, Nucl. Fus. 32 (1994) 611. [6] H. Yuki, et al., J. Phys. Soc. Jpn. 66 (1997) 73; H. Yuki, et al., J. Phys. G 23 (1997) 1459. [7] H. Yuki, et al., JETP Lett. 68 (1998) 765; J. Kasagi, et al., J. Phys. Soc. Jpn. 71 (2002) 277; J. Kasagi, Prog. Theor. Phys., Suppl. 154 (2004) 365. [8] K. Czerski, et al., Europhys. Lett. 54 (2001) 449. [9] F. Raiola, et al., Eur. Phys. J., Appl. Phys. (Online) 13 (2002) 377. [10] S. Ichimaru, Rev. Mod. Phys. 65 (1993) 255. [11] K. Czerski, et al., Europhys. Lett. 68 (2004) 363. [12] G. Gamow, Z. Phys. 51 (1928) 204. [13] R.W. Gurney, E.U. Condon, Phys. Rev. 33 (1929) 127. [14] H.J. Assenbaum, K. Langanke, C. Rolfs, Z. Phys. A 327 (1987) 461. [15] S. Engstler, et al., Phys. Lett. B 202 (1988) 179. [16] S. Engstler, et al., Z. Phys. A 342 (1992) 471. [17] U. Greife, et al., Z. Phys. A 351 (1995) 107. [18] D. Zahnow, et al., Z. Phys. A 359 (1997) 211. [19] A. Krauss, et al., Nucl. Phys., A 465 (1987) 150. [20] H.H. Anderson, J.F. Ziegler, Hydrogen Stopping Powers and Ranges in All Elements, Pergamon, New York, 1977. [21] C. Rolfs, Prog. Theor. Phys. Suppl. 154 (2004) 373. [22] J. Phys. Soc. Jpn. 73 (2004) 608. [23] S. Engstler, et al., Phys. Lett. B 279 (1992) 20.
Low energy nuclear cross sections in metals Jirohta Kasagi Laboratory of Nuclear Science, Tohoku University, Mikamine 1-2-1, Taihaku, Sendai 982-0826, Japan Available online 13 March 2007
Abstract In order to investigate the interplay between nuclei and their surroundings, deuteron induced fusion reactions in a metal environment have been studied at very low energies. We summarize the results of the measurements so far performed: reaction rates of the D(d,p)T reaction in various metals and those of the 6,7Li(d,α)4,5He reaction in Pd and Au. In addition, the kinematic measurements recently performed are also described. These measurements showed that low energy nuclear reactions are strongly affected by the metal environment and huge amounts of energy in the condensed matter scale might be converted to the colliding two-body system. © 2007 Elsevier B.V. All rights reserved.
1. Introduction Effects of the surroundings of a nucleus on nuclear phenomena have been investigated for many years [1]. Usually the observed effect is very small, less than 1% at most. Such smallness is due to the huge difference of the interaction energies; i.e., eV in an atomic system, versus MeV in a nuclear system. However, a surprisingly large effect was claimed in the so-called cold fusion [2], which roused attention more strongly on the influence of the environment where nuclear processes take place. Since then, enhancement of the reaction rates of the D + D reaction during implantation of deuterium in metal has been intentionally searched for. Roth et al. [3] first reported the reaction rate of the D + D → p + t reaction in Ti down to Ed = 3 keV and showed that the deduced excitation function is consistent with no enhancement in the cross section. Kasagi et al. [4] measured the thick target yields for the D(d,p)T and D(d,n)3He reactions in Ti for 4.5 b Ed b 18 keV, and concluded that they were explained well by the cross sections of the data compiled by Bosch and Hale [5]. Yuki et al. [6] succeeded in measuring the reaction rates at lower bombarding energies down to 2.5 keV, and deduced the screening energy of the DD reaction in metal, which is a quantitative scale of the enhancement at very low energies. The screening energy for Yb host (80 eV) is the first evidence for enhanced fusion reaction rate in the metal environment for the keV deuteron bombardment.
E-mail address: [email protected]. 0257-8972/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2006.01.087
Anomalously large values of screening energy were found later for PdO (600 eV), Pd (310 eV) and Fe (200 eV) [7]: the reaction rate for PdO at Ed = 2.5 keV is about 100 times the normal. Such large screening energies for the DD reaction were also found in other materials by other groups. Czersky et al. [8] reported enhanced screening energy of the DD reactions in Ta; it was about 300 eV, and was confirmed by Raiola et al. [9] Ichimaru et al. [10] suggested that hydrogen nuclei in metal are strongly screened, since the electrons both in the metallic dband and the hydrogen induced s-band can contribute to the screening effect. They calculated the effective static potential for hydrogen in Ti and Pd, and proposed that the screening distance between two hydrogen nuclei in metal is much shorter than that for atomic hydrogen. However, the calculated screening energy is only 51 eV for Ti and 75 eV for Pd. Czerski et al. [11] calculated the screening energy for DD reactions in metal by applying a dielectric functional method. Their results including the cohesion effects give larger values of the screening energy in a metal environment, for example about 130 eV for Pd, but less than half of the observed value. One can thus summarize the present situation as follows. Low energy DD reactions are enhanced very much when the reaction occurs in a metal environment. The enhancement may be described by a screening energy and depends strongly on the host material. The mechanism of enhancement is not fully understood, especially for the environment which provides screening energy of the DD reaction of more than 200 eV. All these arguments raised the motivation of further studies to
J. Kasagi / Surface & Coatings Technology 201 (2007) 8574–8578
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parameters. Greife et al. [17], reported measurement at centerof-mass energies down to 1.6 keV and deduced the screening energy to be 25 eV, which is considered to be due to the bound electron, and is consistent with a simple estimation described above as well as an estimation based on a quantum picture. Thus one can say that the screening energy of the DD reaction for a D2 gas target is well understood to be due to bound electrons. 3. D + D reactions in metals 3.1. Experimental method
Fig. 1. Relative yield of protons emitted in the D(d,p)T reaction in five hosts as a function of the bombarding energy; (a) two independent measurements for PdO, (b) for Pd and Fe, and (c) for Au and Ti. In the upper sections, the data normalized to the yield at 10 keV are plotted. In the lower sections, the experimental yields divided by the standard calculations are shown as enhancement factor.
understand the phenomena fundamentally as well as to develop applications. 2. Screening energy of D + D reaction with gas target At energies far below the Coulomb barrier, cross sections of nuclear reactions are essentially dominated by the Coulomb penetration factor [12,13]. However, there are significant cross section enhancements beyond the prediction of barrier penetration [14–18]. These enhancements are qualitatively understood as a screening effect due to bound electrons. In a naive picture, the screening effect may be described quantitatively by a screening energy Us, and the cross section at the center-of-mass energy Ecm is described as rðEcm Þ ¼
S ðEcm Þ expf2pgðEcm þ Us Þg; Ecm
ð1Þ
where S(E) is an astrophysical S-factor, and η(E) = ZTZpα(μc2/ 2E)1/2 is the Sommerfeld parameter; ZT and Zp are atomic numbers of the target and projectile, α is the fine structure constant and μ is the reduced mass. The greater the value of Us, the greater the enhancement and vice versa. D + D reactions have been investigated with gas targets by many authors. Krauss et al. [19], parameterized the S-factors for the D(d,p) and D(d,n) reactions by fitting their data with a quadratic polynomial for 5 b Ecm b 120 keV. Bosch and Hale [5] parameterized the reaction cross sections by using the R-matrix
In order to measure the DD reactions below 10 keV, a high current beam is necessary because the cross sections are very small. We have performed such experiments using a low energy ion beam generator at the Laboratory of Nuclear Science of Tohoku University, as described in our previous work [6,7]. Up to the present, we have measured D + D reactions as a function of bombarding energy between 2.5 and 10 keV to deduce the reaction rates. Various foils were bombarded as host materials, such as Be, Ti, Fe, Cu, Ni, Pd, Sm, Yb, Au and PdO. Protons emitted in the D(d,p)T reactions were detected with a ΔE − E counter telescope consisting of 50- and 200-μm thick Si surface barrier detectors. During measurement at a specific bombarding energy, the yield at 10 keV was measured very frequently at intervals in order to verify the number of target deuterons. We always normalized the proton yield to that at 10 keV measured just before and after the run. 3.2. DD fusion in metals In Fig. 1 we show the relative excitation functions of the D(d,p) T reaction in PdO, Pd, Fe, Au and Ti, to demonstrate that the reaction rates depend strongly on the host materials. As expected from the bare D + D reaction the yields decrease very rapidly as the bombarding energy decreases. We show the standard yield by a dotted curve, which corresponds to the thick target yield calculated for the bare D + D reaction in materials by the following equation. Z Ed Yp ð E d Þ ¼ A ND ð xÞrð E Þð dE=dxÞ1 dE; ð2Þ 0
where σ(E) is the bare cross section parameterized by Bosch and Hale [5] and (dE/dx) is the energy loss curve of deuteron Table 1 Screening energy of the D + D reaction in metals obtained from our measurements Material
Screening energy (eV)
PdO Pd Fe Re Cu Yb Ni Au Ti
600 ± 30 310 ± 30 200 ± 20 200 ± 20 120 ± 20 80 ± 20 80 ± 20 70 ± 20 65 ± 30
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parameterized by Anderson and Ziegler [20]. The yields at lower energies depend on the host material very strongly. In the lower part of Fig. 1, we plot the ratio of the experimental yields to the standard calculation in order to make comparisons more clearly. As seen, the reaction rate in PdO is enhanced very much, whereas the deduced enhancement is very small for Au and Ti. In a naïve picture, the screening effect may be described quantitatively by a screening energy Us and the enhanced cross section is described in Eq. (1). The value of Us so far obtained in our measurements are listed in Table 1. Conduction electrons in metal can be regarded as a Fermi gas moving in a mean field produced by the lattice atoms and electrons. If a nucleus is placed in such an electron sea, the scalar potential produced by the nucleus is screened by the surrounding electrons. The Thomas–Fermi model gives ϕs(r) = Ze / r exp(− ker), where ke is given with the electron density ne and Fermi energy EF as ke = (6πe2ne / EF)− 1/2. The potential can be approximated as ϕs(r) = Ze / r − Zeke for ker ≪ 1, and, thus the screening energy for deuterons in the conduction electrons is estimated as Us = e2ke. The screening energy for a deuteron in the conduction electrons in Fe is estimated as Us = 24 eV in this picture; the value is only 1/10 of the experimentally deduced value. For Pd, Ichimaru et al. [10], including the effects of deuterons in the lattice, calculated the screening energy as Us = 75 eV. The experimental value is about 4 times larger than the calculation. Czerski et al. [11] calculated the screening energy for Pd to be 130 eV, less than half of the experimental value. Thus we conclude that the screening energy for DD fusion reactions in Fe, Pd and PdO cannot be explained by the presently available calculations. It should be stressed that those values are extraordinarily large; i.e., 310 eV for Pd and 600 eV for PdO. A relevant correlation may be that between the screening energy and the deuteron density in the host during bombardment: a large screening energy goes with a small density. In Fig. 2, we plot screening energy vs. inverse of deuteron density, including the data obtained by Rolf's group. The squares are our data [7] and the circles are those of Ref. [21]. Although the data are greatly scattered, a correlation between the screening energy
Fig. 3. Yield ratio of protons to tritons of the D + D→p + t reaction in Au (b), Pd (c) and PdO (d) detected at 145° for bombarding energies between 8 and 20 keV. In (a) the calculated results are shown for the assumption that the target deuteron is in motion toward the beam direction with various kinetic energies from 0 eV to 500 eV. A hatched region indicated in (b), (c) and (d) correspond to the estimated ratio including multiple scattering process.
and the deuteron density may be seen. It should be noted that correlations are clearly seen for the data indicated by larger circles and squares connected by arrows, which are for the same host metal but different density. It should also be pointed out that Pd and its hetero compound always show huge screening energy as follows: 310 eV [7], 800 eV [22], 300 eV [11] and 600 eV [7] for PdO. The density may be related to the diffusivity, or mobility of D+ ions in the host; large mobility results in small density of the target deuterons and large screening energy. We suggest the possibility of a dynamic screening mechanism during the deuteron bombardment and penetration into the host wherein the fluidity of deuterons must play a decisive role. 3.3. Kinematic measurement of the D + D→p + t reaction in metal Since the screening energy for the DD reaction in metals is much larger than the energy scale of the atomic systems, one might expect effects on the kinematic quantities. We have tested the possibility of seeing such an effect in yield ratios of protons to tritons in the D + D→p + t reaction detected with a single detector. The measured ratio is equal to the ratio of the solid angle ratio of protons to tritons which depends only on the bombarding energy as well as the detection angle, shown as follows;
Fig. 2. Screening energy vs. inverse of deuteron density. Our data are plotted with squares and the data reported in [8] are plotted with circles. A pair of large circle and square connected with an arrow is for the same host metal.
ðdr=dXcm Þp ðdXcm =dXlab Þp dNp =dXlab Yp R¼ ¼ ¼ Yt ðdNt =dXlab Þ ðdr=dXcm Þt ðdXcm =dXlab Þt ðdXcm =dXlab Þp ¼ : ðdXcm =dXlab Þt
ð3Þ
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Here, (dσ/dΩcm) is the differential cross section at the detected angle in the cm system and its value is the same for protons and tritons for the D + D → p + t reaction. Thus any deviation of the yield ratio from the kinematic calculation requires a change of the kinematics of the two-body colliding system; for example, the target deuteron is not at rest but in motion before the collision. Yield ratios of protons to tritons have been measured with a Si detector placed at 145° with respect to the beam direction for bombarding energies between 8 and 20 keV. Foils of CD2, Ti, Pd, PdO and Au were bombarded as the host for the DD reaction. In order to obtain statistically significant results, both protons and tritons were accumulated at least 40,000 counts for one run at each bombarding energy and more than 10 runs of the measurements were performed for each foil. In Fig. 3, we show the data for Pd, PdO and Au compared with a preliminary estimation including the multiple scattering, which is shown by the hatched area. Although the multiple scattering reduces the ratio considerably, the data cannot be explained by the estimated values. The largest deviation is observed for PdO shown in Fig. 3(d). We infer that the deviations from the calculation including multiple scattering are due to the motion of the target deuteron in the metal environment. The ratios calculated with a simple assumption that the target deuteron is in a linear motion toward the beam direction are plotted in Fig. 3(a), for kinetic energies of the target deuteron, 0, 50, 100, 300 and 500 eV. It should be noticed that the effect is not negligible but observable even for the energy of 50 eV. Although a precise calculation including multiple scattering is not available yet, the size of the deviation observed in Fig. 3(b), (c) and (d) roughly gives the amount of the kinetic energy of the target deuteron as follows; 50 eV for Au, 150 eV for Pd and 300 eV for PdO. Of particular interest is the correlation of the screening energy and the energy of the target deuteron. Thus, the large screening energy and the motion of the target deuteron might originate from the same source. 4. Screening energy for the Li + D reaction in metal In order to explore the mechanism of enhanced screening, other nuclear reactions have been measured in metal. We have investigated the 6,7Li(d,α)4,5He reactions in metal, for the first time [22]. We selected two metals as hosts in which the Li + d reactions occur; they are Pd and Au. As discussed in the previous section, the screening energy of the D + D reaction in Pd is very large. On the other hand, normal size of screening is obtained for the D + D reaction in Au as Us = 70 ± 10 eV in [7] and 61 ± 20 eV in [21]. The results for the PdLix and AuLix targets are shown in Fig. 4; Fig. 4(a) for PdLix and Fig. 4(b) for AuLix. The upper part of Fig. 4 shows the excitation functions of the 6,7Li(d,α)4,5He reactions relative to the yield at Ed = 75 keV. The standard calculations are plotted with dotted lines in Fig. 4. In the lower part of Fig. 4, we plot the ratio of the experimental yields to the standard calculations in order to make the comparison easier. As seen, the reaction rate in Pd is systematically enhanced for both reactions.
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Fig. 4. Relative yield of α particles emitted in the 6,7Li(d,α)4,5He reaction as a function of the bombarding energy of deuterons; (a) for PdLix and (b) for AuLix. In the upper part, the data normalized to the yield at 75 keV are plotted. In the lower part, the experimental yields divided by those presented with the dotted curve are shown. The dotted curves correspond to the relative yields calculated without screening. Solid curves correspond to calculations with the screening energy indicated in each section.
We deduced the values of Us of the 6Li(d,α)4He and the 7Li (d,α)5He reaction, separately, for each data by fitting the experimental relative yields. The results are Us = 1500 ± 310 and 60 ± 150 eV for the Li + d reactions in Pd and Au, respectively. The calculations with screening energy Us are shown by the solid lines in the upper and lower parts of Fig. 4. The screening energy of the 6Li + d and 6,7Li + p reactions has been obtained in [23] to be 420 ± 120 eV for the LiF target and 350 ± 80 eV for the hydrogen and deuterium gas target. The present work shows, for the first time, that, in a metallic environment, the size of the screening effect in the Li + d reaction depends strongly on the metal host. The obtained value of the screening energy in Pd is about 4 times larger than those mentioned above. As discussed in the previous section, the screened electrostatic potential of the nucleus with atomic number Z existing in the sea of conduction electrons is given as ϕs(r) = Ze / r·exp (− ker); ke = (6πe2ne / EF)1/2, ne is the number density of electrons and EF is the Fermi energy of the electrons. Thus the beam deuteron experiences a reduced Coulomb repulsion force, when
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it collides with the nucleus, and the corresponding screening energy is approximated as Uce = Ze2ke. For the Li + d reaction in Pd metal, EF = 2.66 eV and ne = 1.97 × 1022 cm− 3, thus Uce = 61 eV is expected. The effect of the bound electron should be added, since the Li atom is considered to remain in metal in the form of Li+. Summing up the values of the screening energy due to conduction electrons and bound electrons, we obtain a value of about 230 eV. Even if the experimental value in [12] is used for the bound electrons, the summed value is 410–480 eV. Therefore, the large screening energy of ∼ 1500 eV obtained for the Li + D reaction in Pd cannot be due to electron screening alone. Of particular interest is the fact that the Pd metal provides a large screening effect not only for the Li + d reaction but also for the D + D reaction, whereas the Au metal host does not in both cases. Thus the mechanism of enhanced screening in metal might have the same origin in the D + D and Li + d reactions. Although the enhanced screening is not fully understood, we have previously discussed the possibility that the large screening effect might originate from fluid deuterons in Pd. 5. Summary and outlook Low energy deuteron beams have been used for the study of nuclear fusion reactions in metal environment, since so-called cold fusion was claimed in this environment. Mostly studied is the D + D reaction, in which the implanted deuterons serve as targets for subsequent bombardment with other deuterons. Up to the present, there have been a few discovery steps which bring a significant surprise and raise considerable interest. The first is the fact that the DD reaction rate really depends on the host metal, which was reported in Ref. [6] although the observed change is not very large but certainly larger in Yb than in Ti. The second is the discovery of an anomalously large screening energy for Pd and PdO [7]. The other two groups subsequently and independently found a similar size for the enhanced screening for other metals. Thus one could conclude that D + D reactions in metal can be enhanced immensely and begin a serious exploration of nuclear fusion at room temperature. The screening mechanism so far studied in nuclear-astrophysics cannot explain the reported large screening energies. Therefore other factors to change the reaction rate should be searched for. This might originate from the condition of the surface, temperature of the beam spot, deuteron density, and so on. Experimental development together with theoretical progress is further desirable to reveal the nuclear reaction mechanism in condensed matter. Recent experiments on the Li + D reaction in metal is the first step for expanding nuclear reactions other than the D + D
reaction. The result is very interesting, because the reaction rate is enhanced very much for the Pd host as the D + D reaction. The kinematic measurement of the D + D reaction, which is performed quite recently by our group, gives a convincing result. It clearly shows that deuterons in Pd and PdO gain kinetic energy. It should be emphasized that the method of measuring the yield ratio does not require precisely constancy of the number of target deuterons: this condition is highly desired for the yield measurement. The observed large energy transferred to the motion of target deuterons might originate from the same source of the large screening energy, since there is strong correlation. Nuclear reaction studies with low energy deuteron bombardment on metal surfaces have revealed interesting features of reactions in metal: i.e., large energy transfer from condensed matter to the nuclear system. The large screening energy deduced for the DD reaction in Pd and PdO enables an occurrence of reaction with thermal energy deuterons, if the same condition was made. The large kinetic energy of the target deuteron, again, in Pd and PdO might help to understand the origin of the large screening energy. Further investigations serve to increase our fundamental understanding and to develop many applications. References [1] G.T. Emery, Annu. Rev. Nucl. Sci. 22 (1972) 165. [2] M. Fleischmann, S. Pons, J. Electroanal. Chem. 261 (1989) 301; S.E. Jones, et al., Nature 338 (1989) 737. [3] J. Roth, et al., Nucl. Fus. 30 (1990) 441. [4] Kasagi, et al., J. Phys. Soc. Jpn. 64 (1995) 3718. [5] H.S. Bosch, G.M. Hale, Nucl. Fus. 32 (1994) 611. [6] H. Yuki, et al., J. Phys. Soc. Jpn. 66 (1997) 73; H. Yuki, et al., J. Phys. G 23 (1997) 1459. [7] H. Yuki, et al., JETP Lett. 68 (1998) 765; J. Kasagi, et al., J. Phys. Soc. Jpn. 71 (2002) 277; J. Kasagi, Prog. Theor. Phys., Suppl. 154 (2004) 365. [8] K. Czerski, et al., Europhys. Lett. 54 (2001) 449. [9] F. Raiola, et al., Eur. Phys. J., Appl. Phys. (Online) 13 (2002) 377. [10] S. Ichimaru, Rev. Mod. Phys. 65 (1993) 255. [11] K. Czerski, et al., Europhys. Lett. 68 (2004) 363. [12] G. Gamow, Z. Phys. 51 (1928) 204. [13] R.W. Gurney, E.U. Condon, Phys. Rev. 33 (1929) 127. [14] H.J. Assenbaum, K. Langanke, C. Rolfs, Z. Phys. A 327 (1987) 461. [15] S. Engstler, et al., Phys. Lett. B 202 (1988) 179. [16] S. Engstler, et al., Z. Phys. A 342 (1992) 471. [17] U. Greife, et al., Z. Phys. A 351 (1995) 107. [18] D. Zahnow, et al., Z. Phys. A 359 (1997) 211. [19] A. Krauss, et al., Nucl. Phys., A 465 (1987) 150. [20] H.H. Anderson, J.F. Ziegler, Hydrogen Stopping Powers and Ranges in All Elements, Pergamon, New York, 1977. [21] C. Rolfs, Prog. Theor. Phys. Suppl. 154 (2004) 373. [22] J. Phys. Soc. Jpn. 73 (2004) 608. [23] S. Engstler, et al., Phys. Lett. B 279 (1992) 20.