arXiv subjects

S. Hofmann

Publications and source records attributed to S. Hofmann.

At least 37 records · Page 2Linked to original sources

arXiv2008

Quasifission and fusion-fission in massive nuclei reactions. Comparison of reactions leading to the Z=120 element

The yields of evaporation residues, fusion-fission and quasifission fragments in the $^{48}$Ca+$^{144,154}$Sm and $^{16}$O+$^{186}$W reactions are analyzed in the framework of the combined theoretical method based on the dinuclear system concept and advanced statistical model. The measured yields of evaporation residues for the $^{48}$Ca+$^{154}$Sm reaction can be well reproduced. The measured yields of fission fragments are decomposed into contributions coming from fusion-fission, quasifission, and fast-fission. The decrease in the measured yield of quasifission fragments in $^{48}$Ca+$^{154}$Sm at the large collision energies and the lack of quasifission fragments in the $^{48}$Ca+$^{144}$Sm reaction are explained by the overlap in mass-angle distributions of the quasifission and fusion-fission fragments. The investigation of the optimal conditions for the synthesis of the new element $Z$=120 ($A$=302) show that the $^{54}$Cr+$^{248}$Cm reaction is preferable in comparison with the $^{58}$Fe+$^{244}$Pu and $^{64}$Ni+$^{238}$U reactions because the excitation function of the evaporation residues of the former reaction is some orders of magnitude larger than that for the last two reactions.

nucl-th↗

arXiv2008

Mass measurements in the vicinity of the rp-process and the nu p-process paths with JYFLTRAP and SHIPTRAP

The masses of very neutron-deficient nuclides close to the astrophysical rp- and nu p-process paths have been determined with the Penning trap facilities JYFLTRAP at JYFL/Jyväskylä and SHIPTRAP at GSI/Darmstadt. Isotopes from yttrium (Z = 39) to palladium (Z = 46) have been produced in heavy-ion fusion-evaporation reactions. In total 21 nuclides were studied and almost half of the mass values were experimentally determined for the first time: 88Tc, 90-92Ru, 92-94Rh, and 94,95Pd. For the 95Pdm, (21/2^+) high-spin state, a first direct mass determination was performed. Relative mass uncertainties of typically $δm / m = 5 \times 10^{-8}$ were obtained. The impact of the new mass values has been studied in nu p-process nucleosynthesis calculations. The resulting reaction flow and the final abundances are compared to those obtained with the data of the Atomic Mass Evaluation 2003.

nucl-ex↗

arXiv2007

Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order

In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter to pressureless dust which plays the role of a dynamically coupled observer. The evolution of those observables is governed by a physical Hamiltonian and we derived the corresponding equations of motion. Linear perturbation theory of those equations of motion around a general exact solution in terms of manifestly gauge invariant perturbations was then developed. In this paper we specialise our previous results to an FRW background which is also a solution of our modified equations of motion. We then compare the resulting equations with those derived in standard cosmological perturbation theory (SCPT). We exhibit the precise relation between our manifestly gauge-invariant perturbations and the linearly gauge-invariant variables in SCPT. We find that our equations of motion can be cast into SCPT form plus corrections. These corrections are the trace that the dust leaves on the system in terms of a conserved energy momentum current density. It turns out that these corrections decay, in fact, in the late universe they are negligible whatever the value of the conserved current. We conclude that the addition of dust which serves as a test observer medium, while implying modifications of Einstein's equations without dust, leads to acceptable agreement with known results, while having the advantage that one now talks about manifestly gauge-invariant, that is measurable, quantities, which can be used even in perturbation theory at higher orders.

gr-qc↗

arXiv2007

Dahlberg's bilinear estimate for solutions of divergence form complex elliptic equations

We consider divergence form elliptic operators $L=-\dv A(x)\nabla$, defined in $\mathbb{R}^{n+1}=\{(x,t)\in\mathbb{R}^{n}\times\mathbb{R}\}, n \geq 2$, where the $L^{\infty}$ coefficient matrix $A$ is $(n+1)\times(n+1)$, uniformly elliptic, complex and $t$-independent. Using recently obtained results concerning the boundedness and invertibility of layer potentials associated to such operators, we show that if $Lu=0$ in $\mathbb{R}^{n+1}_+$, then for any vector-valued ${\bf v} \in W^{1,2}_{loc},$ we have the bilinear estimate $$|\iint_{\mathbb{R}^{n+1}_+} \nabla u \cdot \bar{\bf v} dx dt |\leq C\sup_{t>0} \|u(\cdot,t)\|_{L^2(\mathbb{R}^n)}(\||t \nabla {\bf v}\|| + \|N_*{\bf v}\|_{L^2(\mathbb{R}^n)}),$$ where $\||F\|| \equiv (\iint_{\mathbb{R}^{n+1}_+} |F(x,t)|^2 t^{-1} dx dt)^{1/2},$ and where $N_*$ is the usual non-tangential maximal operator. The result is new even in the case of real symmetric coefficients, and generalizes the analogous result of Dahlberg for harmonic functions on Lipschitz graph domains.

math.CA↗

arXiv2007

A proof of the local $Tb$ Theorem for standard Calderón-Zygmund operators

We give a proof of a so-called "local $Tb$" Theorem for singular integrals whose kernels satisfy the standard Calderón-Zygmund conditions. The present theorem, which extends an earlier result of M. Christ \cite{Ch}, was proved in \cite{AHMTT} for "perfect dyadic" Calderón-Zygmund operators. The proof in \cite{AHMTT} essentially carries over to the case considered here, with some technical adjustments.

math.CA↗

arXiv2007

Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty}$ coefficients

We consider divergence form elliptic operators of the form $L=-\dv A(x)\nabla$, defined in $R^{n+1} = \{(x,t)\in R^n \times R \}$, $n \geq 2$, where the $L^{\infty}$ coefficient matrix $A$ is $(n+1)\times(n+1)$, uniformly elliptic, complex and $t$-independent. We show that for such operators, boundedness and invertibility of the corresponding layer potential operators on $L^2(\mathbb{R}^{n})=L^2(\partial\mathbb{R}_{+}^{n+1})$, is stable under complex, $L^{\infty}$ perturbations of the coefficient matrix. Using a variant of the $Tb$ Theorem, we also prove that the layer potentials are bounded and invertible on $L^2(\mathbb{R}^n)$ whenever $A(x)$ is real and symmetric (and thus, by our stability result, also when $A$ is complex, $\Vert A-A^0\Vert_{\infty}$ is small enough and $A^0$ is real, symmetric, $L^{\infty}$ and elliptic). In particular, we establish solvability of the Dirichlet and Neumann (and Regularity) problems, with $L^2$ (resp. $\dot{L}^2_1)$ data, for small complex perturbations of a real symmetric matrix. Previously, $L^2$ solvability results for complex (or even real but non-symmetric) coefficients were known to hold only for perturbations of constant matrices (and then only for the Dirichlet problem), or in the special case that the coefficients $A_{j,n+1}=0=A_{n+1,j}$, $1\leq j\leq n$, which corresponds to the Kato square root problem.

math.AP↗

arXiv2007

Direct mass measurements beyond the proton drip-line

First on-line mass measurements were performed at the SHIPTRAP Penning trap mass spectrometer. The masses of 18 neutron-deficient isotopes in the terbium-to-thulium region produced in fusion-evaporation reactions were determined with relative uncertainties of about $7\cdot 10^{-8}$, nine of them for the first time. Four nuclides ($^{144, 145}$Ho and $^{147, 148}$Tm) were found to be proton-unbound. The implication of the results on the location of the proton drip-line is discussed by analyzing the one-proton separation energies.

nucl-ex↗

arXiv2005

The Spectrum of Fluctuations in Singularity-free Inflationary Quantum Cosmology

We calculate the power spectrum of vacuum fluctuations of a generic scalar field in a quantum cosmological setting that is manifestly singularity-free. The power spectrum is given in terms of the usual scale invariant spectrum plus scale dependent corrections. These are induced by well-defined quantum fluctuations of de Sitter spacetime, resulting in a modified dispersion relation for the scalar field. The leading correction turns out to be proportional to the ratio of Hubble scale and Planck Mass. The maximal relative change in the spectrum is on the ten percent level and might be observable with future CMB experiments.

astro-ph↗

arXiv2003

Signatures in the Planck Regime

String theory suggests the existence of a minimum length scale. An exciting quantum mechanical implication of this feature is a modification of the uncertainty principle. In contrast to the conventional approach, this generalised uncertainty principle does not allow to resolve space time distances below the Planck length. In models with extra dimensions, which are also motivated by string theory, the Planck scale can be lowered to values accessible by ultra high energetic cosmic rays (UHECRs) and by future colliders, i.e. $M_f\approx$ 1 TeV. It is demonstrated that in this novel scenario, short distance physics below $1/M_f$ is completely cloaked by the uncertainty principle. Therefore, Planckian effects could be the final physics discovery at future colliders and in UHECRs. As an application, we predict the modifications to the $e^+e^- \to f^+f^-$ cross-sections.

hep-th↗

arXiv2003

Falconer conjecture in the plane for random metrics

We prove the following variant of the Falconer conjecture in the plane. If the dimension of a compact planar set is greater than one, then the distance set with respect to almost every ellipse has positive Lebesgue measure.

math.CA↗

arXiv2003

Sharp rate of average decay of the Fourier transform of a bounded set

We prove that the spherical mean of the Fourier transform of the characteristic function of a bounded convex set (without any additional assumptions) or a bounded set with a C^{3/2} boundary decays at infinity at the same rate as the Fourier transform of the characteristic function of the ball.

math.CA↗

arXiv2002

Formation of small-scale structure in SUSY CDM

The lightest supersymmetric particle, most likely the lightest neutralino, is one of the most prominent particle candidates for cold dark matter (CDM). We show that the primordial spectrum of density fluctuations in neutralino CDM has a sharp cut-off, induced by two different damping mechanisms. During the kinetic decoupling of neutralinos, non-equilibrium processes constitute viscosity effects, which damp or even absorb density perturbations in CDM. After the last scattering of neutralinos, free streaming induces neutralino flows from overdense to underdense regions of space. Both damping mechanisms together define a minimal mass scale for perturbations in neutralino CDM, before the inhomogeneities enter the nonlinear epoch of structure formation. We find that the very first gravitationally bound neutralino clouds ought to have masses above 10^{-6} solar masses, which is six orders of magnitude above the mass of possible axion miniclusters.

astro-ph↗

arXiv2002

The Role of Mass Asymmetry and Shell Structure in the Evaporation Residues Production

The effects of the entrance channel and shell structure of reacting nuclei on the experimental evaporation residues have been studied by analysing the 40Ar+176Hf, 86Kr+130,136Xe, 124Sn+92Zr and 48Ca+174Yb reactions leading to the 216Th* and 222Th* compound nuclei. The measured excitation function of evaporation residues for the 124Sn+92Zr reaction was larger than that for the 86Kr+130Xe reaction. The experimental values of evaporation residues in the 86Kr+136Xe reaction were about 500 times larger than that in the 86Kr+130Xe reaction. These results are explained by the initial angular momentum dependence of the fusion excitation functions calculated in framework of the dinuclear system concept and by the differences in survival probabilities calculated in framework of advanced statistical model. The dependencies of the fission barrier and the Γ_n / Γ_f ratio on the angular momentum of the excited compound nucleus are taken into account.

nucl-th↗

arXiv2002

Suppression of High-P_T Jets as a Signal for Large Extra Dimensions and New Estimates of Lifetimes for Meta stable Micro Black Holes -From the Early Universe to Future Colliders

We address the production of black holes at LHC in space times with compactified space-like large extra dimensions (LXD). Final state black hole production leads to suppression of high-P_T jets, i.e. a sharp cut-off in the cross section for pp->jet+X. This signal is compared to the jet plus missing energy signature due to graviton production in the final state as proposed by the ATLAS collaboration. Time evolution and lifetimes of the newly created black holes are calculated based on the microcanonical formalism. It is demonstrated that previous lifetime estimates of micro black holes have been dramatically underestimated. The creation of a large number of quasi-stable black holes is predicted with life times beyond hundred fm/c at LHC. Medium modifications of the black holes evaporation rate due to the quark gluon plasma in relativistic heavy ion collisions as well as provided by the cosmic fluid in the early universe are studied.

hep-ph↗

arXiv2001

Quantitative Comparison between AES and SIMS Depth Profiles of a Double Layer Structure of AlAs in GaAs Using the MRI-model

Application of the so called mxing-roughness-information depth (MRI)-model to the quantitative reconstruction of the in-depth distribution of composition is demonstrated by comparing SIMS and AES depth profiles. A GaAs/AlAs reference sample consisting of two layers of AlAs (1 ML and 36 ML) separated by 44 ML of a GaAs matrix was depth profiled using almost identical sputtering conditions: Ar+ ions of 3 keV impact energy and 52 (SIMS: CAMECA 4f) and 58 deg. (AES: VG Microlab 310F) incidence angle. Both the Al+ intensity of the SIMS profile and the Al (LVV) intensity of the AES profile were quantified by fitting the measured profiles with those calculated with the MRI model, resulting in the same mixing length of 3.0 +/- 0.3 nm, similar roughness parameter (1.4-2 nm), and negligible information depth (0.4 nm). Whereas practically no matrix effect was observed for AES as well as for Al+ in the SIMS profile, quantification using dimer (Al2+) and trimer (Al3+) ions shows a marked nonlinearity between concentration and intensity, with the main effect caused by simple mass action law probability of cluster ion formation.

cond-mat.mtrl-sci↗

arXiv2000

Ultimate Depth Resolution and Profile Reconstruction in Sputter Profiling with AES and SIMS

New developments in quantitative sputter depth profiling during the past ten years are reviewed, with special emphasis on the experimental achievement of ultrahigh depth resolution (below 2 nm for sputtered depths larger than 10 nm). In this region, the depth resolution function generally is asymmetric (i.e.non-Gaussian) and it is governed by the three fundamental parameters: atomic mixing length, roughness and information depth. The so called mxing-roughness-information depth (MRI)-model and its application to the quantitative reconstruction of the in-depth distribution of composition, with a typical accuracy of one monolayer and better, is demonstrated for SIMS and AES depth profiles. Based on the combination of the above three parameters, the ultimate depth resolution is predicted to be about 0.7-1.0 nm. Up to now, values of 1.4-1.6 nm have been reported, and the use of low energy molecular ions, e.g. by using sulfur hexafluoride as sputtering gas, has recently pushed the mixing length down to 0.4-0.6 nm. However, particularly in depth profiling of multilayers, it can be shown that minimizing the rouhgness parameter, including the straggling of the mixing length, is most important for the achievement of the ultimate depth resolution.

cond-mat.mtrl-sci↗

arXiv1999

Kaon effective mass and energy from a novel chiral SU(3)-symmetric Lagrangian

A new chiral SU(3) Lagrangian is proposed to describe the properties of kaons and antikaons in the nuclear medium, the ground state of dense matter and the kaon-nuclear interactions consistently. The saturation properties of nuclear matter are reproduced as well as the results of the Dirac-Brückner theory. Our numerical results show that the kaon effective mass might be changed only moderately in the nuclear medium due to the highly non-linear density effects. After taking into account the coupling between the omega meson and the kaon, we obtain similar results for the effective kaon and antikaon energies as calculated in the one-boson-exchange model while in our model the parameters of the kaon-nuclear interactions are constrained by the SU(3) chiral symmetry.

nucl-th↗

arXiv1998

Effective kaon energy from a novel chiral SU(3) model

A new chiral SU(3) Lagrangian is proposed to describe the properties of kaons and anti-kaons in the nuclear medium. The saturation properties of nuclear matter are reproduced as well as the results of the Dirac-Brückner theory. After introducing the coupling between the omega meson and the kaon, our results for effective kaon and anti-kaon energy are quite similar as calculated in the one-boson-exchange model.

nucl-th↗