The limits of the total crystal-field splittings

The crystal-fields causing $|J>$ electron states splittings of the same second moment $\sigma^{2}$ can produce different total splittings $\Delta E$ magnitudes. Based on the numerical data on crystal-field splittings for the representative sets of crystal-field Hamiltonians ${\cal H}_{\rm CF}=\sum_{k}\sum_{q}B_{kq}C_{q}^{(k)}$ with fixed indexes either $k$ or $q$, the potentials leading to the extreme $\Delta E$ have been identified. For all crystal-fields the admissible ranges $(\Delta E_{min},\Delta E_{max})$ have been found numerically for $1\leq J\leq 8$. The extreme splittings are reached in the crystal-fields for which ${\cal H}_{\rm CF}s$ are the definite superpositions of the $C_{q}^{(k)}$ components with different rank $k=2,4$ and 6 and the same index $q$. Apart from few exceptions, the lower limits $\Delta E_{min}$ occur in the axial fields of ${\cal H}_{\rm CF}(q=0)=B_{20}C_{0}^{(2)}+B_{40}C_{0}^{(4)}+B_{60}C_{0}^{(6)}$, whereas the upper limits $\Delta E_{max}$ in the low symmetry fields of ${\cal H}_{\rm CF}(q=1)=B_{21}C_{1}^{(2)}+B_{41}C_{1}^{(4)}+B_{61}C_{1}^{(6)}$. Mixing the ${\cal H}_{\rm CF}$ components with different $q$ yields a secondary effect and does not determine the extreme splittings. The admissible $\Delta E_{min}$ changes with $J$ from $2.00\sigma$ to $2.40\sigma$, whereas the $\Delta E_{max}$ from $2.00\sigma$ to $4.10\sigma$. The maximal gap $\Delta E_{max}-\Delta E_{min}=2.00\sigma$ has been found for the states $|J=4>$. Not all the nominally allowed total splittings, preserving $\sigma^{2}=const$ condition, are physically available, and in consequence not all virtual splittings diagrams can be observed in real crystal-fields.Comment: 30 pages, Appendix (8 pages) and 11 tables; submitted to pss(b

The total energy splitting of ionic eigenstates in the axial crystal fields

The relationship between the energy total splitting $\Delta E$ of the free-ion electron states in the axial crystal-fields and the second moment of that splitting $\sigma^{2}$ is thoroughly investigated. The non-Kramers and Kramers states with the quantum number $1\leq J \leq 8$ in the axial crystal-fields of any multipolar composition but fixed $\sigma^{2}$ are considered. Since the crystal-field Hamiltonian ${\cal H}_{\rm CF}$ is a superposition of the three effective multipoles various $\Delta E$ can correspond to a fixed $\sigma^{2}$ according to the resultant combination of the independent contributions. This $\Delta E$ variation range is the subject of the study. For the states under examination $\Delta E$ can take the values from $2.00\sigma$ to $3.75\sigma$, whereas the difference $\Delta E_{max}- \Delta E_{min}$, except the states with $J\leq 5/2$, amounts roughly to $\sigma$. For comparison, the one-multipolar ${\cal H}_{\rm CF}$s yield accurately defined $\Delta E$ ranging from $2.50\sigma$ to $3.00\sigma$. The limitations of the allowed $\Delta E$ values exclude rigorously a number of virtually possible splitting diagrams. The documentary evidence for this restriction has been supplied in the paper collating the nominally admissible total energy splittings $\Delta {\cal E}$ (i.e. those preserving the $\sigma^{2}$) with the $(\Delta E_{min}, \Delta E_{max})$ ranges occurring in the actual axial crystal-fields. Although the $\Delta E$ unlike the $\sigma^{2}$ is not an essential characteristic and depends on the reference frame orientation, it is useful to know its dispersion range, particularly attempting to assign or verify complex electron spectra.Comment: 17 pages, 4 tables, submitted to pss(b

Capability of the free-ion eigenstates for crystal-field splitting

Any electron eigenstate |\Psi>of the paramagnetic ion open-shell is characterized by the three independent multipole asphericities A_{k}=<\Psi || C^(k)}||\Psi> for k=2,4 and 6 related to the second moments of the relevant crystal-field splittings by \sigma_{k}^{2}=]A_{k}^{2}S_{k}^{2}, where S_{k}^{2}=]\sum_{q}|B_{kq}|^{2}. The A_{k} can serve as a reliable measure of the state |\Psi>capability for the splitting produced by the k-rank component of the crystal-field Hamiltonian and allow one to verify any fitted crystal-field parameter set directly comparing the calculated and the experimental second moments of the relevant crystal-field splittings. We present the multipole characteristics A_{k} for the extensive set of eigenstates from the lower parts of energy spectra of the tripositive 4f^{N} ions applying in the calculations the advanced eigenfunctions of the free lanthanide ions obtained based on the M. Reid f-shell programs. Such amended asphericities are compared with those achieved for the simplified Russell-Saunders states. Next, they are classified with respect to the absolute or relative weight of the A_{k} in the multipole structure of the considered states. For the majority of the analyzed states (about 80%) the A_{k} variation is of order of only a few percent. Some essential changes are found primarily for several states of Tm^{3+}, Er^{3+}, Nd^{3+}, and Pr^{3+} ions. The detailed mechanisms of such A_{k} changes are unveiled. Particularly, certain noteworthy cancelations as well as enhancements of their magnitudes are explained.Comment: 20 pages, 6 table

Stress-related alterations of visceral sensation: animal models for irritable bowel syndrome study.

Stressors of different psychological, physical or immune origin play a critical role in the pathophysiology of irritable bowel syndrome participating in symptoms onset, clinical presentation as well as treatment outcome. Experimental stress models applying a variety of acute and chronic exteroceptive or interoceptive stressors have been developed to target different periods throughout the lifespan of animals to assess the vulnerability, the trigger and perpetuating factors determining stress influence on visceral sensitivity and interactions within the brain-gut axis. Recent evidence points towards adequate construct and face validity of experimental models developed with respect to animals' age, sex, strain differences and specific methodological aspects such as non-invasive monitoring of visceromotor response to colorectal distension as being essential in successful identification and evaluation of novel therapeutic targets aimed at reducing stress-related alterations in visceral sensitivity. Underlying mechanisms of stress-induced modulation of visceral pain involve a combination of peripheral, spinal and supraspinal sensitization based on the nature of the stressors and dysregulation of descending pathways that modulate nociceptive transmission or stress-related analgesic response

A fundamental requirement for crystal-field parametrization

The physically correct parametrization of the energy levels of transition ions in crystals in terms of crystal-field (CF) Hamiltonians ${\cal H}_{\rm CF}=\sum_{k}\sum_{q}B_{kq}C_{q}^{(k)}$ has to be based on the CF parameters $B_{kq}$ that lead to the correct CF splitting second moments, both the global one $\sigma$ and the partial ones $\sigma_{k}$. Only such parametrizations correspond to the appropriate multipolar structure of the surrounding CF. Each parametrization being characterized by its own multipolar crystal-field strengths $S_{k}=(\frac{1}{2k+1}\sum\limits_{q}|B_{kq}|^{2})^{1/2}$, for $k=2,4$ and 6, yields a definite second moment $\sigma$, which can be derived from the additivity relationship $\sigma^{2}=\sum_{k}\sigma_{k}^{2}$ and the known asphericities of the central-ion eigenfunctions $\Psi$. The condition $\sigma=\sigma_{\rm exp}$ must be satisfied to ensure the parametrization's correctness. However, our survey of literature indicates that there exists many other well-fitted crystal-field parameter sets that do not obey this condition. Therefore, such sets are erratic and non-physical, and should be re-examined or rejected. Having $\sigma$ for several $(\geq3)$ eigenstates $|\Psi>$ along with the relevant asphericities, one can estimate $\sigma_{k}$ and $S_{k}$, which are well-founded experimentally. The above findings set up the parametrization process properly. Lack of consistency between the second moments representing various parametrizations and the pertinent second moments observed in experiments is presumably the main reason for deluge of formally accurate but accidental and inequivalent parametrizations.Comment: 10 pages, 2 tables; submitted to pss(b

Transonic small disturbances equation applied to the solution of two-dimensional nonsteady flows

Transonic nonsteady flows are of large practical interest. Aeroelastic instability prediction, control figured vehicle techniques or rotary wings in forward flight are some examples justifying the effort undertaken to improve knowledge of these problems is described. The numerical solution of these problems under the potential flow hypothesis is described. The use of an alternating direction implicit scheme allows the efficient resolution of the two dimensional transonic small perturbations equation

Leki prokinetyczne w Polsce — kiedy i jak stosować?

Leki prokinetyczne dostępne w Polsce stosowane są głównie w chorobach górnego odcinka przewodu pokarmowego, takich jak pierwotne i wtórne zaburzenia motoryki przełyku, choroba refluksowa przełyku, dyspepsja czynnościowa oraz gastropareza. Prokinetyki mają także zastosowanie w czynnościowych zaparciach i zaparciowej postaci zespołu jelita nadwrażliwego oraz w pewnych sytuacjach szczególnych, m.in. przed gastroskopią u chorych z ostrym krwawieniem z górnego odcinka przewodu pokarmowego lub u pacjentów z nietolerancją żywienia dojelitowego. Prokinetyki dostępne w Polsce to itopryd (antagonista receptora dopaminowego D2 i inhibitor acetylocholinesterazy), cyzapryd (agonista receptora serotoninowego 5-HT4) oraz metoklopramid (antagonista receptora D2 i agonista receptora 5-HT4). Dodatkowo właściwości prokinetyczne posiada także erytromycyna jako agonista receptora motyliny. Itopryd (Zirid®, Prokit®) charakteryzuje się minimalnym ryzykiem interakcji lekowych oraz dobrą tolerancją. Stosowanie cyzaprydu (Gaspridu®) wymaga szczególnych środków ostrożności w związku z ryzykiem poważnych działań niepożądanych, w szczególności kardiologicznych. Metoklopramid został wycofany z użycia jako prokinetyk do stosowania przewlekłego ze względu na wiele działań niepożądanych, w tym groźnych powikłań neurologicznych, takich jak dyskineza późna i objawy pozapiramidowe. Erytromycyna podana w jednorazowej dawce przed gastroskopią w trybie pilnym u chorych z krwawieniem z górnego odcinka przewodu pokarmowego ułatwia opróżnianie żołądka z krwi i skrzepów poprawiając warunki badania. Natomiast rutynowe stosowanie prokinetyków nie jest rekomendowane jako uzupełnienie przygotowania jelita do kolonoskopii. Właściwości prokinetyczne wykazuje również trimebutyna (Debretin®, Debridat®, Tribux®, Ircolon ®) poprzez wpływ na receptory opioidowe μ i δ oraz Iberogast — złożony preparat ziołowy. Zarówno trimebutyna, jak i Iberogast są bezpiecznymi oraz dobrze tolerowanymi preparatami, które mogą być stosowane także u dzieci