Trapping probabilities and desorption energies of alkali atoms on a clean and an oxygen covered tungsten (110) surface

Alkali atoms were scattered with hyperthermal energies from a clean and an oxygen covered (θ ≈ 0.5 ML) W(110) surface. The trapping probability of K and Na atoms on oxygen covered W(110) has been measured as a function of incoming energy (0–30 eV) and incident angle. A considerable enhancement of trapping on the oxygen covered surface compared to a clean surface was observed. At energies above 25 eV there are still K and Na atoms being trapped by the oxygen covered surface. From the temperature dependence of the mean residence time τ of the initially trapped atoms the pre-exponential factor τ₀ and the desorption energy Q were derived using the relation: $\text{τ = τ}{}_0\text{exp}\text{(}\text{Q}\text{kT}{}_{\mathrm{<mtext>s</mtext>}}\text{)}$. On clean W(110) we obtained for Li: $\text{τ}{}_0\text{= (8 ±}\text{8}\text{4}\text{) × 10}{}^{\mathrm{?14}}\text{sec}$, Q = (2.78 ± 0.09) eV; for Na: τ₀ = (9 ± 3) × 10^?14 sec, Q = (2.55 ± 0.04) eV; and for K: τ₀ = (4 ± 1) × 10^?13 sec, Q = (2.05 ± 0.02) eV. Oxygen covered W(110) gave for Na: τ₀ = (7 ±3) × 10^?15 sec, Q = (2.88 ± 0.05) eV; and for K: $\text{τ}{}_0\text{= (1.3 ±}\text{0.9}\text{0.6}\text{) × 10}{}^{\mathrm{?14}}\text{sec}$, Q = (2.48 ±0.05) eV. The adsorption on clean W(110) has the features of a supermobile two-dimentional gas; on the oxygen covered W(110) adsorbed atoms have the partition function of a one-dimen-sional gas. The binding of the adatoms to the surface has a highly ionic character in the systems of the present experiment. An estimate is given for the screening length of the non-perfect conductor W(110):k_s^?1≈ 0.5 Å.     

Thermoelectric power measurements in polycrystalline AgI: Cd system

Thermoelectric power of polycrystalline AgI: Cd system was measured as a function of temperature from 50 to 180°C. The heat of transport $\text{Q}{}^1$, intrinsic vacancy concentration c_o and ratio of interstitial to vacancy mobilities in the β phase were deduced under the assumption of no association. The heat of transport $\text{Q}{}^1$ was also temperature dependent in β-AgI: 0.27 eV at 80°C, 0.21 eV at 100°C and 0.17 eV at 120°C. It was estimated that the formation energy of the defect pair h_F was 0.66 ± 0.06 eV and the activation energies for motion of vacancies and interstitials were 0.55 ± 0.03 and 0.38 ± 0.03 eV, respectively. These approximately agree with data reported up to date in single and poly- crystal β-AgI. The heat of transport of vacancies was approximately equal to the activation energy of vacancy migration.     

Cyclotron resonance observation on the electron lenses of molybdenum Fermi surface

Using a previously described transmission method, cyclotron resonance of electrons on the lens of the Fermi surface of molybdenum was observed. The resonance signals were recorded in Azbel-Kaner configuration with the magnetic field B parallel to the (110) plane of a monocrystal of thickness d = 0.15 mm.The effective mass of the electrons was determined as $\text{m>}{}^1\text{= (0.183 ± 0.002)m}{}_0\text{; m}{}^1\text{= (0.261 ± 0.008)m}{}_0$ and $\text{m}{}^1\text{= (0.29 ± 0.02)m}{}_0$ for B at angles of 0°; 3°; and 7.4° with respect to the crystallographical 〈110〉 direction. For these orientations of B and applying the method of cyclotron resonance cut-off observation, the dimensions of the electron lens were determined.     

A study of the (00) LEED beam intensity at normal incidence from CdS(0001), Cu(001), Cu(111), and Ni(111)

A Faraday cage apparatus is used for the measurement of the (00) LEED beam intensity, I₍₀₀₎, and the total secondary emission coefficient, δ(E_k), for angles of incidence from 0° ± 2° to 8° ± 2°, with an energy resolution of ± 0.037 of the incident beam energy, in the energy range 1 to 200 eV. The data are normalized and expressed as a fraction of the incident beam intensity. The basic principle of operation is the separation of the incident and specularly diffracted beams in a uniform magnetic field. Monolayer, or in-plane, resonances associated with the emergence of nonspecular beams, as well as beam threshold minima, are observed in I₍₀₀₎ at normal incidence from clean CdS(0001), Cu(111), and Ni(111). Some major differences are observed in the I₍₀₀₎ profiles for the clean (111) surfaces of nickel and copper. All secondary Bragg peaks, except the 2$\text{2}\text{3}$ order, have greater intensities for Ni(111) in the energy range 50–150 eV, thus indicating that the atomic scattering cross-section for electrons in this energy range is larger for nickel than for copper. For the (111) surface of nickel, the (11) resonance is missing, but the (10) resonance and all $\text{1}\text{3}$ order secondary Bragg peaks between the second and fifth orders are observed. For Cu(111) both the (10) and (11) resonances are observed, but the $\text{1}\text{3}$, $\text{2}\text{3}$, 1$\text{2}\text{3}$, and 3$\text{1}\text{3}$ order secondary Bragg peaks are missing in this energy range. These data indicate that multiple scattering with evanescent intermediate waves, or “shadowing”, is predominate on the (111) surfaces on nickel and copper for energies above 30 eV, and that below 30 eV multiple scattering with propagating intermediate waves is predominate on Cu(111). Correlation of the (00) beam intensity profiles from clean Ni(111) at 0°, 2°, and 6° with the intensity profiles of the (10). (1&#x0304;0), and (11) non-specular beams is nearly one-to-one from 30 eV to 100 eV, thus supporting the dynamical theories of LEED in which peaks in the (00) beam are expected to occur at nearly the same energies as peaks in the non-specular beams.     

The stability of W2 and WRe adatom clusters on (110) tungsten surfaces

Kinetics of formation and dissociation of W₂ and WRe adatom clusters and dissociation reaction equilibria on (110) W were studied by field ion microscopy. Deposits of two adatoms only on the (110) face of a tungsten FIM tip were used and these reached an equilibrium state at 400 K. For the W₂ dissociation reaction $\text{ΔA}{}^{\mathrm{?}}\text{(430}\text{K}\text{) = 30 ± 5}\text{kJ mol}{}^{\mathrm{?1}}$; for WRe dissociation $\text{ΔA}{}^{\mathrm{?}}\text{(400}\text{K}\text{) = 14 ± 2}\text{kJ mol}{}^{\mathrm{?1}}$. The dissociation energies indicated by kinetics were consistent with these values.     

Atom-surface scattering with velocity-selected H and D atomic beams from LiF and NaF (001)

Hydrogen and deuterium atoms with an energy between 20 and 140 meV have been scattered from LiF and NaF (001) cleavage planes in UHV. The atomic beam was nearly monoenergetic by use of a slotted disk type velocity selector with a velocity resolution of $\text{Δv}\text{v}\text{=12\%}$ (FWHM). The scattering showed diffraction with a pronounced specular beam. The energies of several bound surface states have been determined by analysis of selective adsorption minima. These energies together with relative intensities of diffracted beams and specular intensity versus incident energy measurements may be represented by an interaction potential of Morse-type with additional terms which are periodic parallel to the surface. The parameters of the Morse-potential have been found to be: depth D=17.8 meV and reciprocal range $\text{κ=1.04}\text{A}\text{?}{}^{\mathrm{?1}}$ for H₁/LiF (001) and D = 17.9 meV, k = 1.15 Å^?1 for H₁/NaF (001); the additional periodic terms have relative strength β₁₀=0.04 and $\text{β}{}_{11}\text{≈}\text{β}{}_{10}\text{2}$ in the case of H ₁/LiF, but β₁₁≈β₁₀=0.03 in the case of H₁/NaF. From the observed influence of surface temperature on the position of selective adsorption minima the coefficient of thermal expansion of the topmost surface layer turns out to be approximately twice the bulk value.     

Measurement of charge distributions for 229Th(nth,f) and 232U(nth,f)

A gas ΔE ? E_R telescope has been used to measure charge yields and their correlations with kinetic energies for ²²⁹Th and ²³²U. Even-charge yields are enhanced compared with odd-charge yields for both fissioning systems; this enhancement increases for events with higher kinetic energy. The mean odd-even effect $\text{δ}{}_{\mathrm{<mtext>p</mtext>}}\text{is}\text{= (40±4)\%}\text{for}{}^{229}\text{Th}$; it is $\text{(21 ± 3)\%}\text{for}{}^{232}\text{U-the same as for}{}^{233}\text{U}\text{((22.1±2.1)\%)}\text{and}{}^{235}\text{U}\text{((23.7±0.7)\%)}$. The energy-integrated δ_p and δ_p for different energy windows, vary strongly as a function of charge (Z) due to the underlying shells. The δ_p averaged over Z increases fast with kinetic energy, contrary to the existing results for ²³³U and ²³⁵U, where δ_p flattens off at low energies. For both systems, the most probable kinetic energy ē shows a strong odd-even stagger; the mean odd-even effect on energy, $\text{δE}{}_{\mathrm{<mtext>K</mtext>}}{}^{\mathrm{<mtext>o?e</mtext>}}\text{,}\text{is}\text{1.4 ± 0.3}\text{MeV for}{}^{229}\text{Th, and}\text{1.7±0.4}\text{MeV for}{}^{232}\text{U}\text{—}$ the latter is about twice the value for ${}^{233}\text{U}\text{(0.95 ± 0.09}\text{MeV}\text{)}\text{and}{}^{235}\text{U}\text{(0.7}\text{MeV}\text{)}$. These results are discussed in terms of the existing models.     

Interaction of neutral hydrogen atoms with KCl(OO1)

Neutral hydrogen atoms with velocity selected thermal energies, have been scattered from KCl(001) cleavage planes in UHV. For cold crystal surfaces (T_SF ? 170 K) even a small residual pressure of water resulted in an ordered monolayer coverage of the (001) plane. From this surface, diffraction has been observed with diffracted beams up to third order and characteristically varying intensities were observed and analysed in terms of a quantum mechanical rainbow scattering theory. Resonant transitions of atoms to bound states at the surface (“selective adsorption”) were observed and used to determine the interaction potential of hydrogen atoms with this water covered surface: first in terms of a Morse potential, second in terms of a $\text{C}{}_3\text{z}{}^3$-dependent attractive potential. The surface Debye-Waller factor has been measured for clean KCl(001), for the water covered (001) plane as well as for partially covered surfaces. The results are interpreted within a simple model.     

A LEED determination of the structures of Ru(001) and of CORu(001)−√3 × √3 R30°

The structures of Ru(001) and of the √3 × √3 R30° overlayer of CO on Ru(001) have been determined by LEED I–V measurements and comparison to calculations. Special attention was paid to accurate angular alignment, selection of a well-ordered portion of the surface, and avoidance of beam-induced changes of the CO layer. Five orders of reflexes over a range of 300 eV each were used for the clean surface and 7 orders over 200 eV each for the CO superstructure. For the clean surface, a slight contraction of the first layer spacing (by 2%) was found which gave r-factors of 0.04 (Zanazzi-Jona) and 0.16 (Pendry) for 5 non-degenerate beams. For the CO structure the most probable geometry is the on-top site with spacings $\text{d(}\text{RuC}\text{) = 2.0 ± 0.1}\text{A}\text{?}\text{and}\text{d(}\text{CO}\text{) = 1.10 ± 0.1}\text{A}\text{?}\text{(r}{}_{\mathrm{<mtext>ZJ</mtext>}}\text{= 0.21; r}{}_{\mathrm{<mtext>P</mtext>}}\text{= 0.51)}$. The two threefold hollow and the bridge sites can be clearly excluded.     

The γ-ray decay properties of low-lying levels of 65Zn via the 65Cu(p,nγ)65Zn reaction

They γ-ray decay of 13 low-lying levels of ⁶⁵Zn has been studied utilizing the ⁶⁵Cu(p, nγ)⁶⁵Zn reaction. The decay scheme was obtained from θ_γ = 90° yield curve measurements and from a neutron-gamma coincidence measurement. Angular distributions γ-rays were measured for seven angles at E_p = 3.5 and 4.0 MeV. Gamma-ray energies, level energies, and branching ratios obtained are compared with recent measurements. Expected angular correlations for possible spin sequences are calculated utilizing Hauser-Feshbach statistical reaction theory. The results, combined with other available evidence, establish the J^π assignments for the following levels: $\text{768.9 ± 0.1}\text{keV}\text{(}\text{5}\text{2}{}^{\mathrm{?}}\text{), 864.8 ± 0.2 (}\text{7}\text{2}{}^{\mathrm{?}}\text{), 1047.5 ± 0.1 (}\text{5}\text{2}{}^{\mathrm{?}}\text{), 1252.9 ± 0.4 (}\text{7}\text{2}\text{and}\text{1343.9 ± 0.1 (}\text{5}\text{2}{}^{\mathrm{?}}\text{)}$. Previous assignments are confirmed for the levels $\text{909.8 ± 0.1}\text{keV}\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{)}\text{and}\text{1369.5 ± 0.2 (}\text{5}\text{2}{}^{\mathrm{+}}\text{)}$. Limiting ifJ-values are obtained for the levels of $\text{1577.1 ± 0.2}\text{keV}\text{(≦}\text{5}\text{2}\text{)}\text{and}\text{1588.2 ± 0.4 (≦}\text{7}\text{2}\text{)}$. Gamma-ray multipole mixing ratios are extracted for 19 transitions between low-lying levels and transition strengths calculated where the level lifetimes are assumed to be in the range 10^?12 to 10^?13 sec.     

The 7Li(d, n0)8Be reaction with polarized 800 keV deuterons

The analysing power of the ${}^7\text{Li}\text{(}\text{d}\text{, n}{}_0\text{)}{}^8\text{Be}$ reaction for vector and tensor polarization of an 800 keV deuteron beam, as well as the relative cross section for the unpolarized beam were measured at 7 to 9 angles between 0° and 160°, using a thick target. Analysis in terms of (l, s, J^π) matrix elements shows that two intermediate states with $\text{J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{+}}$ and $\text{J}{}^{\mathrm{\pi }}\text{=}\text{5}\text{2}{}^{\mathrm{?}}$ present, strongly interfering with each other. Assignments to known ⁹Be levels and to threshold resonances as suggested by Hackenbroich and Seligman are briefly discussed. The magnitude of the vector analysing power makes the reaction interesting as a monitor for the vector polarization of low-energy deuteron beams.     

Valence band parameters and free exciton reduced mass of zinc telluride derived from free exciton magnetoreflectance

Reflectance spectra were measured on ZnTe in magnetic fields up to 18 T for B ? [100] and B ? [110]. The experiments yield renormalized valence band parameters $\text{γ}{}^1{}_2\text{= 0.83 ± 0.08}$ and $\text{γ}{}^1{}_3\text{= 1.30 ± 0.12}$, corresponding to bare parameters γ₂ = 0.95 ± 0.09 and γ₃ = 1.48 ± 0.14. From the free exciton Rydberg energy $\text{R}{}^1{}_0\text{= 12.8}\text{meV}$ we derive a reduced exciton polaron mass m₀ 0.080 ± 0.005 and a bare reduced mass m₀ 0.074 ± 0.005, corresponding to $\text{γ}{}^1{}_1\text{= 3.9 ± 0.7}$ and γ₁ = 4.4 ± 0.7 for an electron effective polaron mass $\text{m}{}^1{}_{\mathrm{e}}\text{= 0.116 m}{}_0$. We further calculate the exciton diamagnetic shift rate according to existing low-field theories modified by a variational calculation taking into account polaron effects and valid up to γ ? 1. The difference between experiment and theory is 10% and the agreement is considered satisfactory.     

The ft value of the superallowed Fermi decay 46V(β+)46Ti

The${}^{46}\text{Ti}\text{(p, n)}{}^{46}\text{V}$ reaction threshold has been measured as 8007.7 ± 1.8 keV, equivalent to an energy release of 6030.6 ± 1.8 keV in the beta decay${}^{46}\text{V}\text{(β}{}^{\mathrm{+}}\text{)}{}^{46}\text{Ti}$. The ${}^{46}\text{V}$ half-life has been measured as 422.28 + 0.23 ms. The corresponding ft value is reasonably consistent with those of other superallowed Fermi decays.     

Interactions of CO molecules adsorbed on oxidised Cu(111) and Cu(110)

Reflection absorption infrared spectroscopy has been used in conjunction with LEED and surface potential measurements to study low temperature CO adsorption on the oxidised Cu surfaces Cu(111)O|$\text{3}\text{2}\text{?}\text{2}$|, Cu(110)O(2 × 1) and Cu(110)Oc(6 × 2). On all three surfaces adsorption at 80 K yields surface potential changes in excess of 0.6 V and does not lead to the formation of an ordered overlayer. At high coverages the adsorption enthalpy is lower than on the clean surfaces. Infrared spectra show the growth of a doublet band with components initially at 2100 and 2117 cm^?1 on the oxidised Cu(111) surface. Similar features seen on the oxidised Cu(110) surfaces are accompanied by a band at 2140 cm^?1: a very weak band at the same frequency on oxidised Cu(111) is attributed to defect sites. Studies of the temperature dependence of the spectrum from oxidised Cu(111) lead to the conclusion that two different binding sites are occupied. Spectra of ${}^{12}\text{CO}{}^{13}\text{CO}$ mixtures show that the molecules occupying these sites are in close proximity to each other, and that the spectrum is subject to large but opposing coverage-dependent frequency shifts.     

Uniaxial stress effects on the 3.4 eV optical structure of silicon by schottky-barrier electroreflectance

The electroreflectance of Si under uniaxial stress has been measured in the 3.0–4.0 eV region at 77 K. The results indicate that the dominant structure in this energy region is attributed to Λ^v₃ → Λ^c₁ (or L^v_3′ → L^c₁ transition. The deformation potentials of these bands are determined to be $\text{D}{}^1{}_1\text{= -7 ± 3 eV,}\text{D}{}^3{}_3\text{= 4 ± 1 eV}\text{and}\text{D}{}^5{}_1\text{= 5 ± 2 eV}$.     

Electron capture decay of 245Bk (4.90 d) and 246Bk (1.80 d)

The electron capture decay schemes of ²⁴⁵Bk and ²⁴⁶Bk have been investigated by measuring the γ-ray and conversion-electron spectra of mass-separated ²⁴⁵Bk and ²⁴⁶Bk samples. The γ-ray spectra were measured with a 25 cm³ Ge(Li) spectrometer and the conversion-electron spectra were measured with a cooled Si (Li) detector. Multipolarities of most of the transitions in ²⁴⁵Cm and ²⁴⁶Cm were deduced. The half-lives of ²⁴⁵Bk and ²⁴⁶Bk were determined by following the decay of the 252.85 and 798.7 keV photopeaks and were found to be 4.90 ± 0.03 d and 1.80 ± 0.02 d, respectively. The α/(α+EC) ratio for the ²⁴⁵Bk decay was measured to be (1.2 ± 0.1) × 10^?3. On the basis of the present investigation the following non-rotational states were identified in ²⁴⁵Cm: $\text{7}\text{2}{}^{\mathrm{+}}$ [624], 0; $\text{5}\text{2}{}^{\mathrm{+}}$[622], 252.85; $\text{1}\text{2}{}^{\mathrm{+}}$ 355.95; $\text{3}\text{2}{}^{\mathrm{?}}$ vibrational, 633.65; and $\text{1}\text{2}{}^{\mathrm{+}}$[620], 740.95 keV. The $\text{3}\text{2}{}^{\mathrm{?}}$ state at 633.65 keV is int as a K_π = 2^? phonon coupled to the i$\text{7}\text{2}{}^{\mathrm{+}}$[624] single-particle state. Our measurements of ²⁴⁶Bk γ-ray and conversion-electron energies and intensities confirm previous level assignments in ²⁴⁶Cm.     

Interference effects in 12C(p, γ)13N and direct capture to unbound states

Excitation functions of the capture reaction ¹²C(p, γ₀)¹³N have been obtained at θ_γ = 0° and 90° and E_p = 150–2500 keV. The results can be explained if a direct radiative capture process, E1(s and d → p), to the ground state in ¹³N is included in the analysis in addition to the two well-known resonances in this beam energy range $\text{[E}{}_{\mathrm{p}}\text{= 457(}\text{1}\text{2}{}^{\mathrm{+}}\text{)}$ and 1699 $\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{) keV]}$. The direct capture component is enhanced through interference effects with the two resonance amplitudes. From the observed direct capture cross section, a spectroscopic factor of C²S(l = 1) = 0.49 ± 0.15 has been deduced for the $\text{1}\text{2}{}^{\mathrm{?}}$ ground state in ¹³N. Excitation functions for the reaction ${}^{12}\text{C(p,γ}{}_1\text{p}{}^1\text{)}{}^{12}\text{C}$ have been obtained at θ_γ = 0° and 90° and E_p = 610–2700 keV. Away from the 1699 keV resonance the capture γ-ray yield is dominated by the direct capture process E1 (p → s) to the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. Above E_p = 1 MeV, the observed excitation functions are well reproduced by the direct capture theory to unbound states (bremsstrahlung theory). Below E_p = 1 MeV, i.e., E_p → 457 keV, the theory diverges in contrast to observation. This discrepancy is well known in bremsstrahlung theory as the “infrared problem”. From the observed direct capture cross sections at $\text{E}{}_{\mathrm{p}}\text{? 1 MeV}$, a spectroscopic factor of C²S(l = 0) = 1.02 ± 0.15 has been found for the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. A search for direct capture transitions to the $\text{3512 (}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$and $\text{3547 (}\text{5}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound states resulted in upper limits of C²S(l = 1) ≦ 0.5 and C²S(l = 2) ? 1.0, respectively. The results are compared with available stripping data as well as shell-model calculations. The astrophysical aspect of the ¹²C(p, γ₀)¹³N reaction also is discussed.     

Angular resolved photoemission from intrinsic surface states on Al (100)

Using photon energies of 11.7, 16.8 and 21.2 eV, we have recorded angular resolved photoemission spectra from clean Al (100). A dominant, surface sensitive peak is interpreted as emission from a two-dimensional band of surface states. The band mass is $\text{m}{}^1\text{=(1.03±0.10)m}$, and the band minimum, (2.8±0.2) eV below E_F for surface momentum k₆=0, is located within the bulk band gap. The observed existence of the peak for large values of k₆, indicates a transition from a true surface state to a surface resonance.     

Optical detection of cyclotron resonance of electron and holes in CdTe

Cyclotron resonance of electron and holes have been optically detected at 70 GHz and at 1.8 K in n-type CdTe. The bare effective masses, in unit of the free electron mass, are found to be: $\text{m}{}^1\text{= 0.088 ± 0.004}$, $\text{m}{}^1{}_{\mathrm{lh}}\text{= 0.12 ± 0.01}$, $\text{m}{}^1\text{= 0.60 ± for H // <100>}$, and $\text{m}{}^1{}_{\mathrm{e}}\text{= 0.089 0.004}$, $\text{m}{}^1{}_{\mathrm{lh}}\text{= 0.11 ± 0.01}$, $\text{m}{}^1{}_{\mathrm{hh}}\text{= 0.69 ± 0.02}$ for H // <111>. The Luttinger valence band parameters deduced from these measurements are: γ₁ = 5.3 ± 0.5, γ₂ = 1.7 ± 0.3 and γ₃ = 2.0 ± 0.3, in fair agreement with the calculations of Lawaetz.     

Measurement of Cl and N quadrupole coupling in ClCN

J = 1 ← 0 and J = 2 ← 1 transitions in ³⁵ClCN and ³⁷ClCN were measured using a C-band waveguide spectrometer and phase-locked sources. Parameters obtained from the data are: $\text{B(}{}^{35}\text{ClCN) = 5 970.820 ± 0.010 MHz}$, $\text{B(}{}^{37}\text{ClCN) = 5 847.246 ± 0.008 MHz}$, $\text{eqQ(}{}^{35}\text{Cl) = ?83.26 ± 0.04 MHz}$, $\text{eqQ(}{}^{37}\text{Cl) = ?65.61 ± 0.04 MHz}$ and $\text{eqQ(}{}^{14}\text{N) = ?3.60 ± 0.08 MHz}$.