De Wette Research Articles

Kritiker und Exegeten: Porträtskizzen zu vier Jahrhunderten alttestamentlicher Wissenschaft.

Kritiker und Exegeten: Porträtskizzen zu vier Jahrhunderten alttestamentlicher Wissenschaft.

Grundgeschichte und Chronik

The Chronicler used two types of sources in writing history: In general, the chronistic narration is based on the „Deuteronomistic history“ as it is called today. Nonetheless, the Pentateuch in its priestly components is another key to its concept.
 In his historical outline, the Chronicler is aware of differences of time: There is, first of all, the epoch of Moses and of the Mosaic institutions given to a wandering Israel. A new age, second, started with David gathering a scattered people toward the new center in Jerusalem.
 These epochs are characterized by both continuity in the worship of Yhwh and discontinuity of theperformance of that worship. The ark, the mobile sanctuary in the tent of the desert, was now to find its definite place and house, to be built and inhabited by Yhwh, prepared by David and finally realized by Solomon.
 According to the Chronicler, God’s word had been present in both epochs, but in different forms. Originally, it was given orally to Moses. Yet, the history of Israel as described by Chronicles refers to written documents (kakkātûb). In light of their attribution in Chronicles we should not call them „priestly“ – as it has been customary since the 19th century (de Wette, Wellhausen) –but more adequately „Mosaic“ tradition.
 For the Chronicler, such Mosaic tradition was applied and performed by David’s Israel. Of prime importance is the new position of Levi, Moses’ own tribe. According to the P-sources in the Pentateuch, the Levites had to do physical labour for the holy tent. But, in the era of the temple, they gained a new responsibility by interpreting, instructing and applying Tora in its broadest sense. The Priests's duties for their part are presupposed rather than itemized. Since the time of the Exodus – which is deliberately not a topic in Chronicles – they have remained the same.
 Decisive for the Chronicler is the new presence of Moses’ revelation in the ongoing history of Israel and its kings, accompanied and guided by Moses’ tribe, the Levites.

The Pentateuch: Genesis

The PentateuchGenesis Christopher T. Begg and Fred W. Guyette 1207. [Genesis–Joshua: P and D] Pekka Pitkäanen, "Reconstruction [sic! Reconstructing] the Social Contexts of the Priestly and Deuteronomic Materials in a Non-Wellhausian Setting," Paradigm Change in Pentateuchal Research, 323-35 [see #1595]. This paper has outlined a possible way of looking at and reconstructing the social context of the Priestly and Deuteronomic materials in a setting that does not assume the main Wellhausian scheme of development and dating of the pentateuchal materials. Such an examination is clearly, if not naturally, linked with dating and compositional issues that relate to the ancient document that is the Pentateuch. Accordingly, I have outlined how such an alternative reconstruction can be linked with the wider isagogical issues. I have above all suggested that priests and Levites as cultic personnel were responsible for creating Genesis–Joshua in the context of Israel's settling the Canaanite highlands and creating a new society there to replace existing indigenous societies. Such a reconstruction [End Page 403] is certainly different from the Wellhausian one; nevertheless, it builds on the idea that a variety of sources were available to the authors from which they created the document we have before us in the Pentateuch. I hope this paper can stimulate further discussion about the Pentateuch in a context that is not limited to the Wellhausian paradigm that in my view is a hindrance when trying to understand this amazing work from antiquity and the history of ancient Israel. Any new understandings may also then have related new ethical, religious, and political implications for today (and also implications for academics). I believe that the above considerations, together with the other presentations that form the basis of this volume, do present a plausible and credible alternative to the Wellhausian approach, which, at a minimum, accounts very well for the data as a whole. [Adapted from published abstract] 1208. [Pentateuch; Roman Law] Matthias Armgardt, "Why a Paradigm Change in Pentateuch Research Is Necessary. The Perspective of Legal History," Paradigm Change in Pentateuchal Research, 79-91 [see #1591]. In this essay, A., a legal historian, makes the case that after two hundred years of scholarly work on the basis of critical foundation of M. W. L. de Wette and a more or less modified Wellhausenian paradigm, pentateuchal research has reached a dead end. The methodological flaws of the enterprise, among them circular reasoning in particular, are obvious. Interestingly, something similar happened in the discipline of the study of Roman Law. After decades of searching for interpolations in the Corpus Iuris Civilis (CIC), about 30 years ago legal historians became aware that there was something wrong with the methods and assumptions that formed the foundation of their research. Today, almost every scholar of Roman Law assumes that the legal texts in the Digest have not, in fact, been interpolated, unless there is really strong evidence to the contrary. If all the theories about interpolations that scholars in the first decades of the 20th century assumed had been correct, the making of the CIC would have taken at least 30 years, not three years. A. further notes that in the case of the CIC there is no doubt that some interpolations did occur, but not nearly as many as earlier scholars suspected. Nowadays, everybody wonders how it is possible that brilliant scholars could have walked into the trap of arbitrariness and uncontrolled speculation in this field of research. A. suggests that a similar turning point has come for Pentateuch research now. A critical analysis of the assumptions and methods of this field of research is needed. At the same time, it is clear that a change of paradigm is never easy. A help in this critical situation is the fact that groundbreaking work has already been done, in particular by Kenneth Kitchen. He, among others, has shown that the right way forward in pentateuchal studies is to rely on external evidence, esp. that from the 2nd millennium b.c.e. In this connection, A. points out that attempts to show a connection between the 1st millennium Vassal Treaties of Esarhaddon or the Law of Gortyn or the Roman Twelve...

Философия религии В. Де Ветте: религиозное чувство и пути его постижения

Философия религии В. Де Ветте: религиозное чувство и пути его постижения

Происхождение Пятикнижия: традиция и Документальная гипотеза

В статье рассматривается проблема происхождения Пятикнижия. Согласно традиционному церковному взгляду, Пятикнижие всегда считалось произведением пророка Моисея. Однако уже в XVII веке - первой половине XVIII века появились исследователи (Бенедикт Спиноза, Ришар Симон, Жан Астрюк), утверждавшие, что весь текст Пятикнижия или отдельные его части не принадлежат пророку Моисею. Эти предположения получили дальнейшее развитие в трудах протестантских ученых Вильгельма Де Ветте, Э. Рейсса, Карла Графа, Г. Гупфельда и Ю. Велльгаузена. В результате Ю. Велльгаузен сформулировал гипотезу, согласно которой текст Пятикнижия состоит из четырех источников (документов): Ягвиста (J), Элогиста (E), Девтерономиста (D) и Жреческого Кодекса (P). Эта гипотеза получила название Документальной. Важно отметить, что самый ранний из этих источников, Ягвист, датируется Ю. Велльгаузеном IX в. до Р. Х. Таким образом, налицо очевидное противоречие между традиционным и критическим взглядами на происхождение книг Закона. Автор статьи излагает основные аргументы адептов Документальной гипотезы, отстаивающих компилятивный характер Пятикнижия, и пытается проследить отношение к ней в отечественной дореволюционной библеистике, католицизме и традиционном иудаизме. In the article the problem of Pentateuch’s origin is researched. According to the traditional Church position, the Pentateuch was always considered a work of the prophet Moses. But already in XVII century - first half of XVIII century they were scholars (Benedictus Spinoza, Richard Simon, Jean Astruc), who argued, that the entire text of Pentateuch or some of its parts do not belong to Moses. These assumptions received a development in the works of protestant scholars Wilhelm De Wette, E. Reuss, Karl Graf, G. Hupfeld and J. Wellhausen. As a result, J. Wellhausen formulated a hypothesis, that the Pentateuch’s text consists of four sources (documents) - Jahwist (J), Elohist (E), Deuteronomist (D) and Priesterkodex (P). This hypothesiswas called the Documentary hypothesis. It is important to notice, that the earliest of these sources was dated by Wellhausen to the IX century BC. So there is an obvious contradiction between the traditional and critical views on the Torah’s origin. The A. sets forth the main arguments of the followers of the documentary hypothesis, who argue a composite character of the Pentateuch, and tries to understand the attitude towards it in pre-revolotionary Russian biblical studies, in Catholicism and traditional Judaism.

Worn like an amulet: black exorcisms of whiteness in recent South African fiction

This article considers black reflections on whiteness in some recent South African fiction, Julian de Wette's novel A Case of Knives (2010. Cape Town: Umuzi) and Zoë Wicomb's Playing in the Light (2006. Johannesburg: Umuzi). Central to these texts are elaborations on the idea of the quotidian. In these novels, everyday life appears through focalizing agents, which suggest how to intellectualize black people's dealings with the ethical dilemmas created by whiteness as a concept generated by apartheid's social engineering. The selected novels archive these accounts within the act of storytelling, especially as this is foregrounded in fantasy as a confidential ‘return’ to and an exorcizing of episodes of black depersonalization. Commenting on this type of reversion to the history of humiliation, the article relies on the image of the ‘return to the harbour’ – drawn from A Case of Knives.The suggestion is also that each relapse highlights ‘fantasy’ as ritual which manifests itself in those discourses in which black people are heard or seen, in private, revealing claims about how they outmanoeuvred whiteness. A Case of Knives depicts these tactics in tragi-comic tones inclining towards satirical representations of apartheid's delineation of whiteness. By contrast, Playing in the Light, which also reflects upon these machinations, explores in a nuanced way the sense of devastation that afflicts black people upon discovering the long-term consequences of European colonialism on black women and their nuclear families. Throughout this article, emphasis is placed on showing that, as seen through the ideas of the ‘return’ and of ‘fantasy’, the concept of ritual is fragile and paradoxical. This is because the selected novels intimate that ritual is destined to be retold in the terms that present blackness as a quintessential nervous condition.

쉐레쉐브스키 주교와 초기 한글성경 : 전도서 1장을 중심으로

Born as a Lithuanian Jew and an American immigrant, Bishop Samuel Isaac Joseph Schereschewsky (1831- 1906) has deeply influenced Chinese and Korean Christians with two of his Bible translations, that is the Peking Colloquial Old Testament (1875) and the Easy Wenli Version (1902). More specifically, the Korean Revised Version (1938) and Gale’s Korean translation (1925) were heavily indebted to his Easy Wenli Version in terms of their dicta and wordings. In case of the Korean Revised Version (1938), about 60% of its wordings have been influenced by Bishop Shereschewsky’s Easy Wenli Bible (1902).<BR> Schereschewsky was given the title of a mission bishop by the American Episcopal Church after he completed the Peking Colloquial Old Testament (1875). He participated in the project to translate the Bible in colloquial Mandarin. In this project he was in charge of translating the Old Testament because of his excellent knowledge of Hebrew and Aramaic. During his translating job, he consulted many commentaries written by Jewish medieval scholars such as Rashi and Ibn Ezra. He also read many German commentaries written by German scholars like de Wette because he had a background of German scholarship that he had gotten in Germany during his teenage years. <BR> His second Bible translation in classic Chinese, Easy Wenli Version (1902), was done by his first Old Testament Version together with the Delegates’s Version in Wenli (1854). As a matter of fact, his first Chinese translation can be said to be the mother version of the Chinese Union Version (1919), which is still in use by Chinese Christians. His second version in Easy Wenli heavily influenced earlier Korean Bibles like the Revised Version (1938) and Gale’s Version (1925). Moreover, his Easy Wenli Bible, together with the Wenli Delegate’s Version, was used by Korean theologians like Rev. Choi Pyung Hun for his theology of indigenization.<BR> In summary, Bishop Schereschewsky was a pioneer in Bible translation in China and Korea by the turn of the last century. Two of his Bibles should be acknowledged as landmarks for Bible translations in Asia.

The "Discovered Book" and the Legitimation of Josiah's Reform

The story of the (or scroll) in the course of the temple restoration at Jerusalem holds a central place in the description of Josiah's reform (2 Kings 22-23). In a dissertation written in 1805, W. M. L. de Wette identified the of the Law as the Book of Deuteronomy and pointed out the close correspondence between the Deuteronomic laws and the cultic reform carried out by Josiah. He therefore argued that the discovered scroll had been composed not long before its discovery.1 Following his suggestion, an enormous amount of literature was dedicated to the analysis of the episode and its historical significance. The seventhcentury date established by de Wette for the of the Law (Deuteronomy) was accepted by the majority of scholars, who considered the discovery a manipulation to push forward the execution of the reform.2 The scope of the discovered scroll is hotly disputed today, but the term of the Law must have referred to a pre-Deuteronomic early work, the so-called Urdeuteronomium.3 Recently, however, Katherine Stott has argued that the of the Law never actually existed outside the pages of the of Kings, and that its mention is a literary stratagem to bolster the credibility of the story within its literary context.4 Was the discovered scroll a virtual work, with no such document in fact existing? Stott presents three Hellenistic and Roman episodes that relate how authors who tried to give credibility to their innovative historical works invoked ostensibly discovered old works on whose evidence their innovations rested.5 Yet how does Stott know that the three discovered books were virtual artifacts? After all, an author who claims to have an unknown ancient source that contradicts the currently known evidence might expect the request to present it for examination by experts, and would naturally prepare a copy of the discovered text. The majority of scrolls, tablets, and books discovered in antiquity were real artifacts that were presented to the audience.6 Stott's suggestion that the three discovered sources are in fact artifacts that never existed is no more than guesswork. Further, the legitimation of a historical is quite different from that of a historical event. The story of Josiah's reform relates how the book was discovered, presented to the king, and later read in public. The story mentions the book eleven times, under different names (2 Kgs 22:8, 10, 11, 13, 16; 23:2, 3, 21, 24). The narrator's emphasis on the reality of the scroll as the force that moved forward the sequence of events and its decisive role in the legitimation of the cult reform is in marked contrast to the suggestion that the was a virtual artifact. History is replete with episodes that can serve as analogies to almost any possible theory; the presentation of analogy in itself does not prove anything. Stott brings no evidence that proves the relevance of the three Hellenistic and Roman episodes she presents for analyzing the account of Josiah's reform. Hence, we may dismiss her claim, tak- ing as a point of departure for this discussion the commonly held assumption that the discovered scroll was a real artifact presented to the king and literati of Judah.7 In what follows I will examine in detail three important points pertaining to the finding of the scroll and the function of the discovery in the story of Josiah's reform: first, the distribution of discovery stories in the ancient Near East and its bearing on the biblical story; second, the verification of artifacts by way of a divine oracle; and, third, the legitimation the scroll bestowed on the cult reform. I. The Discovery of Scrolls and Tablets in the Ancient Near East The manipulation of texts for political and propagandistic purposes as well as the discovery of texts in order to legitimize a present claim were well known in the ancient Near East long before Josiah's reform. …

A simple general proof of the Krazer–Prym theorem and related famous formulae resolving convergence properties of Coulomb series in crystals

The Krazer–Prym theorem extending the Poisson summation formula to oblique lattices is proved as a direct consequence of translational symmetry. A generalized Ewald approach based on this theorem is reproduced. The two other famous approaches proposed by Nijboer and De Wette, and by Harris and Monkhorst, are derived in the same fashion. The absence of any uniform contribution to bulk electrostatic potentials in each of those treatments is emphasized as a property of locally neutral systems subject to translational symmetry. It is found that an analytic evaluation of the Ewald variable parameter naturally follows from the treatment of the Coulomb lattice characteristic in terms of the Krazer–Prym theorem. The extension of those characteristics to off-lattice points is also discussed.

Religion and the Rise of Historicism: W.M.L. de Wette, Jacob Burckhardt, and the Theological Origins of Nineteenth-Century Historical Consciousness, by Thomas Albert Howard

"Religion and the Rise of Historicism: W.M.L. de Wette, Jacob Burckhardt, and the Theological Origins of Nineteenth-Century Historical Consciousness, by Thomas Albert Howard." Canadian Journal of History, 36(1), pp. 145–146

Anti-Jewish Interpretations of Psalm 1 in Luther and in Modern German Protestantism

This article presents a detailed analysis of the different forms of anti-Jewish interpretations of Psalm 1 by M. Luther and in Modern German Protestantism (as exemplified by W. M. L de Wette, E. W. Hengstenberg, H. Hupfeld, B. Duhm, R. Kittel, H. Gunkel, A. Weiser, and H. -J. Kraus). These commentaries reviewed fall into three models of interpretation. The first model is marked by positive interpretation and Christian appropriation. In this model the Jews are deemed incapable of attaining the theological level of the Psalm, because—and reducing what these interpreters say to its essence—the Jews in their strict adherence to nomism cut themselves off from the Christian truth. The second model is that of religio-historical degeneration. The distinguishing feature of this model is that the Psalm is seen as the product of a “decayed post-prophetic Judaism.” The third model is that of religio-historical progression. In contrast with the Hebrew-Jewish level of religious development, which is characterized as external and superficial, Christian religiousness is seen as more spiritual, more inward, and thus it is considered higher on the religious scale. If one were to look for a common basis of the anti-Jewish statements of these exegetes, a decisive factor, in my opinion, is Christology, more specifically, the Reformation’s justification-Christology with its exclusivist, anti-Jewish configuration.

Jacob Burckhardt, Religion, and the Historiography of "Crisis" and "Transition"

Jacob Burckhardt, Religion, and the Historiography of “Crisis” and “Transition” Thomas Albert Howard* A great historical subject, the representation of which should be the high point of a historian’s life, must cohere sympathetically and mysteriously to the author’s innermost being. Jacob Burckhardt 1 If you are to venture to interpret the past you can do so only out of the fullest exertion of the vigor of the present: only when you can put forth your ... qualities in all their strength will you divine what is worth knowing and preserving in the past. Friedrich Nietzsche 2 The renowned nineteenth-century Swiss-German historian Jacob Burckhardt (1818–97) was a masterful historian of crises and transitional periods. Two of his major works, The Age of Constantine the Great (1852) and The Civilization of the Renaissance in Italy (1860), bear out this claim. In his Constantine Burckhardt deals with the transition from late pagan antiquity to the early Christian Middle Ages, and in his more famous Renaissance he deals with the transition from the late Middle Ages to the beginnings of secular modernity. In the [End Page 149] latter, as is well known, he established one of the most compelling and creative theses in the history of modern historiography, virtually creating the “idea of the Renaissance” that has long influenced both scholarly and popular conceptions of that period. 3 What elicited Burckhardt’s interest in crises and transitions in general and in these two periods of crisis and transition in particular? In this article, I shall argue that there is a strong relationship between Burckhardt’s own historical experience in the early and mid-nineteenth century and his choice of subject and mode of analysis in these two monumental works. In theoretical terms one observes a “dialectical” form of objectivity in the execution of Burckhardt’s historiographical tasks: a structural affinity or kinship between subject (Burckhardt, his historical experience) and object (late antiquity, Renaissance) predisposes Burckhardt to his theme/argument and thus provides a key to understanding the genesis and the character of insights that he offers in these two works. 4 To establish this point I shall focus on the category of religion, on Burckhardt’s own experience of questions of religious truth and skepticism in the nineteenth century, and on his treatment of religion in these two works. The Young Jacob Burckhardt and Religion Religion is a crucial but often neglected aspect of Jacob Burckhardt’s thought. 5 Like a number of nineteenth-century German intellectuals, Burckhardt was a Pfarrersohn, a “pastor’s son.” 6 He grew up in a profoundly conservative Protestant environment in Basel, nicknamed “pious Basel” for its dogged resistance to the “ideas of 1789” and for its earlier heritage of Reformation and pietist religiosity. During Burckhardt’s youth in fact, his father was a children’s minister and head-deacon (Obersthelfer) before becoming in 1838 the city cathedral’s Antistes, the highest and most prestigious ecclesiastical office in Basel. In short, as his biographer Werner Kaegi has noted, Burckhardt’s early [End Page 150] upbringing and education were strongly shaped by the world of his father, a world of “old Protestant piety.” 7 Following his father’s example, Burckhardt started out on the clerical track, studying theology at the University of Basel. However, during his Theologie-studium (1837–39) he experienced a profound crisis of faith brought on by an encounter with German historical biblical criticism and liberal theology represented in the person of W. M. L. de Wette (1780–1848). A radical theologian and biblical scholar, de Wette had wound up in Basel in 1822 after being dismissed from the University of Berlin for holding views considered heterodox and politically threatening by the conservative Prussian government. 8 In a letter to his friend Johannes Riggenbach written in August 1838 Burckhardt tells how de Wette’s critical theology had unseated his faith. “In my eyes,” Burckhardt wrote, de Wette’s system grows in stature every day; one simply must follow him, there is no alternative; but every day a part of our traditional church doctrine melts away under his hand. Today, finally, I realized that he regards the birth of Christ simply as a myth...

Periodic boundary conditions and the fast multipole method

The seminal work of Nijboer and De Wette [Physica 23, 309 (1957)] enables the calculation of lattice sums of spherical harmonics, but has long been overlooked. In this article, their central result is recast in a simplified form suitable for modern multipole algorithms that employ the solid harmonics. This formulation makes possible the imposition of periodic boundary conditions within modern versions of the fast multipole method, and other fast N-body methods. The distinction between the extrinsic values obtained with the lattice sums ℳ of the multipole interaction tensors, and the intrinsic values associated with Taylor’s expansion of the Ewald formulas, is made. The central constants, ℳ, are computed to 32 digit accuracy using extended precision arithmetic. Timings and corresponding errors obtained with a periodic version of the fast multipole method are presented for particle numbers spanning [103,106], and a range of expansion orders. A qualitative comparison is made between the present implementation, other periodic versions of the fast multipole method, and fast Ewald methods.

A comparison of Ewald summation techniques for planar surfaces

Ewald-like summation methods to compute the electrostatic Coulomb potential and the forces on charged particles in a two-dimensional periodic system with nonperiodic extension to the third dimension are investigated. The techniques by Hautman and Klein, Mol. Phys. 75 (1992) 379 (HK), Heyes, Barber, and Clarke, J. Chem. Soc. Faraday Trans. II 73 (1977) 1485 (HBC), and Nijboer and de Wette, Physica A 125 (1984) 275 (NdW) are compared in respect to their numerical accuracy and efficiency. The convergence behaviour of the methods is analysed for different magnitudes of the nonperiodic z-separation between the charged particles up to twice the length of the square simulation cell. The HK method is best suited for small z but becomes inefficient for large particle separations in the nonperiodic direction. HBC is not sensitive on the out-of-plane separation but is very slow. NdW is only suited for large out-of-plane distances because it fails completely if the z-separation of any two particles becomes zero. Ready-to-implement sets of equations for the three algorithms are presented in the appendices.

A renormalization method for the evaluation of lattice sums

A number of problems in solid state physics and materials science can be resolved by the evaluation of certain lattice sums (sums over all sites of an infinite perfect lattice of some potential energy function). One classical example, the calculation of lattice sums of circular and spherical harmonics, dates back to the last century, to Lord Rayleigh’s work on computing the effective conductivity of a simple composite. While Lord Rayleigh presented an efficient asymptotic method for two-dimensional problems, he resorted to direct evaluation of the lattice sums in the three-dimensional case. More recent methods, based on Ewald summation, have been developed by Nijboer and De Wette, Schmidt and Lee, and others. In this article, a fast method for evaluating lattice sums which is based on a new renormalization identity is described.

Phonons on fcc (100), (110), and (111) surfaces using Lennard-Jones potentials: I. Comparison between molecular dynamics simulations and slab technique calculations

The surface phonon dispersion curves have been calculated for fcc (100), (110), and (111) surfaces using molecular dynamics (MD) simulations and Lennard-Jones pair potentials. In the low-temperature limit these MD simulations have been compared to the results from slab-technique lattice dynamics calculations of the type pioneered by Allen, Alldredge and de Wette. We compare the dispersion results between these two methods as a prelude to MD studies of the dispersion curves at elevated temperatures. At temperatures where the dynamical behavior is well described within the harmonic approximation, the two techniques should provide equal descriptions of surface phonon spectral densities and phonon frequencies. In this paper we demonstrate this agreement.

Past, Present and Future in Lamentations Iii 52-66: the Case for a Precative Perfect Re-Examined

The possibility of the existence of a precative perfect in Biblical Hebrew-a verb in the perfect used as an optative to express a wish or a hope-was, so far as I have been able to discover, first seriously discussed in the middle of the 19th century by the grammarians Gesenius, Ewald and Bottcher,2 though the idea had already appeared in the work of earlier scholars such as W. M. L. de Wette, in his commentary of 1811 on the Psalms.3 In the 5th edition of Ewald's Hebrew grammar, the first in which the author seems clearly to envisage such a use of the perfect, we find the following:

Surface phonons; past, present and future

The history, present status and prospects for the future of surface phonon research are discussed. The seminal work of Frits de Wette and his students is reviewed. The systems studied up to the present time and some unresolved issues are presented. Two areas where important new advances are anticipated are illustrated by a brief description of recent work in the author's laboratory. A soft-mode was recently found on the W(001) surface and its observed temperature dependence is directly related to the well known reconstruction on this surface. The driving force for the reconstruction can be attributed to a charge density wave for which there is direct evidence. The other area involves the study of phonons of thin single crystal metal films. He atom phonon studies show many modes, whose number increases with the layer thickness up to seven layers.

On the energy per particle in three- and two-dimensional Wigner lattices

We come back to the 1979 controversy about the value of the energy per particleФ, in an infinite Wigner lattice of electrons in a uniform compensating background. For simplicity we restrict ourselves to the simple cubic (and square) lattice. We present an accurate calculation of the energyФel of one electron in the field of the other electrons plus background for the case that the system (system I) is considered as an infinite arrangement of neutral cubes (Wigner-Seitz cells). The value obtained is checked by computer calculations. We confirm the conclusion of de Wette that for this system the relationФi=1/2Фel (often accepted without discussion) does not hold and we calculate the differenceΔФ, which represents the average potential in the system. On the other hand, if the system is considered as the limit of a set of spheres with increasing radii, such that the spheres are neutral (system II), we obtain a different value ofФel and in this caseФi=1/2Фel. We show explicitly that the Ewald method of summation, used by Fuchs and others, leads to the same analytical expression as the limit obtained for a set of neutral spheres (system II). We extend the calculations to the two-dimensional square lattice. Here the equalityФi=1/2Фel holds also in the case of an infinite arrangement of neutral squares (system I).

Surface dynamics of relaxed (001) slabs of alkali halides and MgO.

We have performed a comprehensive study of the lattice dynamics of the unrelaxed and relaxed (001) surfaces of the alkali halides and MgO. The dynamical calculations were carried out for 15-layer slabs, for which the surface relaxation had been evaluated in earlier work [F.W. de Wette, W. Kress, and U. Schr\oder, Phys. Rev. B 32, 4143 (1985)]. Both the relaxation calculations and the dynamical calculations were based on the same shell models for the alkali halides, available in the literature. The results for the surface-mode frequencies at the high-symmetry points \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}, X\ifmmode\bar\else\textasciimacron\fi{}, and M\ifmmode\bar\else\textasciimacron\fi{} of the surface Brillouin zone (SBZ) are presented, and compared with the corresponding frequencies for unrelaxed slabs. In addition, for those compounds not treated in the calculations of Chen, de Wette, and Alldredge [Phys. Rev. B 15, 1167 (1977)] for unrelaxed alkali halide slabs (NaBr, KF, KCl, KBr, KI, RbBr, and RbI) as well as for RbF, we also present dispersion-curve diagrams for wave vectors along the boundary \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} X\ifmmode\bar\else\textasciimacron\fi{} M\ifmmode\bar\else\textasciimacron\fi{} of the irreducible part of the SBZ. In general the relaxation-induced changes in the surface-mode frequencies are small; the largest changes for each compound are found for the optical surface mode with polarization perpendicular to the surface (${\mathrm{SP}}_{\mathrm{\ensuremath{\perp}}}$). Moreover, as a general rule, the effects of relaxation on the surface dynamics are largest for the heavy compounds; these have the largest ionic polarizabilities and exhibit the largest surface relaxation. The most pronounced relaxation-induced changes in the surface dynamics occur for RbF, RbBr, and RbI. In RbF the optical surface mode ${\mathrm{SP}}_{\mathrm{\ensuremath{\perp}}}^{\mathrm{\ensuremath{-}}}$, which lies in the optical-acoustical gap, undergoes a substantial upward shift as a result of the relaxation, while in RbBr and RbI the same optical surface mode ${\mathrm{SP}}_{\mathrm{\ensuremath{\perp}}}$ is pushed above the bulk continuum. These three should be the most interesting cases for experimental study by inelastic He scattering. Experimental confirmation or lack of confirmation of these predictions will provide important information about suitability of bulk interaction models for use in surface dynamical calculations.